Octopuses, squids, cuttlefish, and nautiloids make up the class Cephalopoda (Greek: head-feet). Cephalopods appear in oceans, horror stories, nineteenth-century polemical literature, and—in their Mormon instantiations—in my next four posts.  I begin with the cuttlefish.
Since cuttlefish eject a cloud of brown fluid to confuse predators (see image below) and then flee, authors sometimes used the cuttlefish as a stand-in for cowardice and hypocrisy.  Consider the following (non-Mormon-related) example:
Much more deeply scorned, then, is a cold, flabby, slimy cuttlefish of a man, or class of men who fear to meet an issue squarely, but at the slightest alarm, attempt to hide an ignominious retreat under a cloud of ink. Nowhere, not even in the depths of the ocean, are there any more cowardly or contemptible creatures than the cuttlefish of the Chicago daily press. They have gone down in disgraceful defeat before Zion and her General Overseer many times in the last thirteen years, but have never failed to attempt to cover their retreat with a cloud of their slimy, black ink—a mass of shameful, stupid lies. 
Moral and/or metaphysical extrapolations from physiology and ecology were widespread in the nineteenth century and are probably present as subtext in the examples below. Note also the apparent irresistibility of the ?cloud of ink? / journalist connection.
I have identified only two instances of anti-Mormon cuttlefish rhetoric. In describing Mormonism in 1913, one John D Nutting wrote that Mormonism was ?often little understood, and more often wrongly understood? because, among other reasons, it ?conceals itself like a cuttlefish.?  In 1896 an author took a more naturalistic tack: ?It is said that one drop of liquid from a cuttlefish can cloud a ton of water, but the moral poison of Mormonism only has spreading power amid ignorance that is already dense.? 
I found four instances of Mormon authors using cuttlefish imagery, all emphasizing deception. The most extended came from an editorial entitled ?Cuttle Fish Hypocrisy,? which criticized ?professed ?preachers of righteousness?? who ?forever continue to slander the Mormon people? because ?they [the preachers], like the cuttle-fish, are desirous of concealing themselves? and ?anxious to have the minds of the people turned from the shallowness of their own false systems.?  Another piece attacked anti-polygamist politicians: ?those villainous human cuttle-fish use the cry of polygamy to hide their real motives, and that it alone may be seen until they have secured what they are actually aiming at—the power and the possessions of the ?Mormons.?? 
In a different vein, there was a Mormon hymn—?I?m a Merry-hearted Mormon,? by William Willes—with a list of sea creatures, including cuttlefish and devil-fish, metaphorically caught in the Mormon proselyting net cast from ?the good ship Zion.? The fifth of seven stanzas reads:
We?ve cat-fish and dog-fish and lobsters and crabs, And cuttle-fish and devil-fish and thorn-backs and dabs; Many scorpions and pollywogs and crocodiles grim, With shoals of big sea-hogs fill the net to the brim.
The song was sung in General Conference in 1866, published in a hymnal in 1872, and reproduced in anti-Mormon books in 1882 and 1884. 
Cuttlefish metaphors were not specific to Mormon or anti-Mormon discourse; I found instances in various contexts.  I did not find, however, any reference to the cuttlefish?s ability to change color, which sort of surprises me since it?s, well, cool, and fits into the deception and hypocrisy idea so well (see image above).  Also, though cuttlefish were plentiful, widely distributed, and well-known for thousands of years, nineteenth-century polemicists sometimes felt it necessary to describe the cuttlefish before using it in arguments (most people would have never seen one).
I also did not find or come up with any persuasive reasons for why or when the cuttlefish metaphors appeared—other than as a device to liven up arguments long since stale. 
 The octopus has continued as a polemical device through the present. My study period is approximately 1820 to 1920. The image of the cuttlefish in profile comes from the NOVA program at PBS, “Anatomy of a Cuttlefish.”
 Image: Andy Carter, ?Cuttlefish shooting ink,? near Tenerife, Canary Islands, 2008 Aug 12, Flickr. See also, Thomas P. Peschak, ?A pharaoh cuttlefish releases a plume of ink as it is stabbed by a diver?,? Daymaniyat Islands Nature Reserve, Oman, published at National Geographic. Because of the pigmented cloud, our word ?sepia? comes from the Latin/Greek word for ?cuttlefish.? Cuttlefish also have chromatophores which enable them to change color for camouflage, but I did not find any references to this ability in the nineteenth-century literature.
 The text preceding the quoted section: ?The cuttlefish, when alarmed always beats a hasty retreat, throwing out a great cloud of black ink, to hide its movements. There is no use blaming the creature for its cowardice. It is weak and soft; its blood is cold; it has a very rudimentary brain; and, no matter what the occasion, can only attempt offense or defense by squirting out the gloom of its Plutonic ink. Still it is not a pleasant object to contemplate. Men with warm, red blood in their veins usually have a profound, withering contempt for a coward, even if the craven is only a beast or a fish. Much more deeply scorned, then?.? AWN, ?Literary Cuttlefish,? Leaves of Healing 13:17 (1903 Aug 15): 544-545, paragraphing altered. The periodical Leaves of Healing was the organ of a restorationist religious movement headed by John Alexander Dowie (the ?General Overseer? mentioned above), headquartered at Zion, IL.
 ?Mormonism has been called ?Satan?s masterpiece;? and, with all respect to its sincere adherents, there is no more fitting name. It is often little understood, and more often wrongly understood; for it is far away from most people, is many-sided, conceals itself like a cuttlefish, and is spread over such an area as to make local study and generalization difficult. He who would understand Mormonism must either be content to spend years in study and first-hand observation among the common people and in reading publications for and against it, or he must take the results of such study and experience on the part of others who have so studied.? John D Nutting, ?Mormonism To-Day and Its Remedy,? The Missionary Review of the World 36:4 (1913 Apr): 247 (247-256); volume is numbered as ?Old Series,? vol 36:4 and ?New Series,? vol 26:4.
 ??Wyoming and Nevada may be, to some degree, politically honey-combed by Mormon influences; but it hardly seems that this once dreaded power will have much effect on the moral progress of the American people. It is said that one drop of liquid from a cuttlefish can cloud a ton of water, but the moral poison of Mormonism only has spreading power amid ignorance that is already dense; and while it cannot be denied that the Morons have materially improved the wilderness in which they settled, it must not be forgotten that, since the death of Brigham Young, Gentile schools have sprung up all over Mormon territory, and the new generation have not that blind adherence to the Elders of that church which would prevent their consorting?.? The Illustrated American 19 (1896), p 99 [snippet only]. Though the ink-cloud is a viable defense mechanism, I think earlier writers vastly overstated its density and size.
 A 250-word excerpt from an 800-word editorial: ?When the cuttle fish wishes to hide his true position it opens its spleen bag of black gall and squirts the inky substance into the water around it. There are, in the so-called Christian world of the nineteenth century, a great many professed ?preachers of righteousness,? who take a delight (apparently so, from the numerous instances thereof,) in using the same methods, and going through the same manoeuvres as the cuttle fish, when they wish to turn the public mind against that system of religion erroneously known as ?Mormonism.? This ?cuttle fish hypocrisy? on the part of our good ?Christian? friends is neither sound or convincing. Preachers may rant and rage about ?Mormonism;? they may howl and storm from their lofty pulpits; but after they have foamed and frothed, and their boiling anger is somewhat cooled, they look down upon this strange, peculiar sect called ?Mormons,? and behold! they grow, increase, and multiply in numbers. ? Why do modern Christians forever continue to slander the Mormon people, and fail to give reason or Scripture for so doing? It is simply this, they, like the cuttle-fish, are desirous of concealing themselves, they are anxious to have the minds of the people turned from the shallowness of their own false systems, hence they belch forth wild anathemas against the Latter-day Saints, hiding themselves at the same time behind this sectarian fog of error, heresy, vile abuse, and misrepresentation. They define ?Mormonism? as being a system of lust, false, heinous, treacherous and vile. ?? No author listed, ?Cuttle Fish Hypocrisy,? Latter Day Saints Southern Star 2:24 (Chattanooga, TN, 1900 May 12 Sat): 188.
 In reference to ?Governor Murray and his clique?: No author listed, ?Governor Murray and the ?Mormons?,? The Latter-day Saints? Millennial Star 43:45 (1883 Oct 22 Mon): 681 (680-682). A few months later: ?No person has tried harder, nor resorted to more unscrupulous methods of late, to bring trouble upon the Saints, than has Governor Murray. We have several times alluded to his actions and pointed out his motives. In writing about him a few months since, we compared him to a cuttle-fish, which, to hide his own nefarious character from observation, exudes an inky fluid. Recent developments have tended to prove that the comparison was a just one.? G. C. L., ?Threatening Clouds,? The Latter-day Saints? Millennial Star 46:8 (1884 Feb 25 Mon): 121 (120-121); ?But we cannot feel to have patience with any cuttle-fish methods of politics—attempts to blame others for results which have been largely promoted by the evasive and unscrupulous complainants themselves.? No author listed, ?As to Statehood,? The Deseret Weekly 48:9 (Salt Lake City, 1894 Feb 17): 266.
 No author listed, ?Minutes of the Thirty-sixth Annual Conference of the Church of Jesus Christ of Latter-day Saints,? The Latter-day Saints? Millennial Star 28:22 (1866 Jun 02 Sat): 338 (337-340). William Willes, The Mountain Warbler: Being a Collection of Original Songs and Recitations with Selections from Other Writers, for the Use of Choirs, Sabbath Schools and Families (Salt Lake City: Deseret News, 1872), 43-44. Walter Gore Marshall, Through America: Or, Nine Months in the United States, new and cheaper edition (London: Sampson Low, Marston, Searle, & Rivington, 1882), p 210. William Jarman, Appendix B [excerpts from The Mountain Warbler], U.S.A.: Uncle Sam?s Abscess, or Hell upon Earth for U.S. Uncle Sam (Exeter, England: H Leduc?s Steam Printing Works, 1884), 188.
 A non-Mormon usage in a Mormon context: ?But Mr. Sherman, who demonetized silver, has adopted the cuttle-fish policy and is attempting to deceive and abuse the miners throughout the west.? Senator Stewart [presumably William Morris Stewart], speech to the Salt Lake City Chamber of Commerce, 1891 Sep 17, as printed in ?The Silver Question,? The Deseret Weekly, Salt Lake City, 1891 Sep 26 Sat, p 445 (444-446). An RLDS use of cuttlefish as example of God?s giving to all things means of self-defense: ?The cuttlefish can make the sea like ink about it, and escape in the confusion in which it has enveloped its pursuer.? Jordan B Chute, ?Meekness,? The True Latter Day Saints? Herald 23:7 (Plano, IL, 1876 Apr 01): 196. The cuttlefish appears in an allegedly-Mormon hymn including list of sea creatures as metaphorically caught in the Mormon proselyting net: Walter Gore Marshall, Through America: Or, Nine Months in the United States, new and cheaper edition (London: Sampson Low, Marston, Searle, & Rivington, 1882), p 210. Cuttlefish also appeared in thoroughly non-Mormon contexts: ?? after showing up the foggy style of expression on great fundamental doctrines, as though the function of language was to conceal our thoughts—as if there were a special pleasure in enacting the part of the cuttle-fish, and hiding himself in his own ink—he says?.? No author listed, review of E Mellor, The Atonement: Its Relations to Pardon, 2nd ed (London: Hamilton, Adams, and Co, 1869), in The Gospel Herald 38 (1869 Jun 01): 142; ?Though each doughty hero cuffed the other soundly, yet both, with true Spartan tenacity, held the secret intact; neither mentioned the well known name of Peyrère, but, like the cuttle-fish, purposely obscuring the water, each alluded to the French Calvinistic Protestant as an ?Italian Monk.?? William Pinkerton, ?Traditions of an Antecedent World,? Notes and Queries, 3rd Series, vol 7 (London, 1865 Feb 18): 141; [of an address delivered at a meeting of the American Institute of Homeopathy:] ?We do not wish to misrepresent Dr. Wilson, and think we do not, but, like the cuttle-fish, he often surrounds himself with so dark a medium that it is very difficult to see exactly where he is. Hence, perhaps, in part at least, may have arisen the misconceptions of his auditors and the press, of which he complains.? JHM, ??The Rejected Address?—A Review,? The Hahnemannian Monthly 7:3 (1871 Oct): 99 (97-106).
 Photograph of Sepia latimanus (Reef cuttlefish) with dark coloration (left) seconds before changing to light coloration (right), Nick Hobgood [Nhobgood], 2006 Sep 02, (CC-BY-SA-3.0 or GFDL), via Wikimedia Commons.
 I did not find a reasonable place to stick the following references into the post. File them under ?Tangential Mormon Cephalopod Connections?:
A. Octopuses were sometimes called devil fish, which was also a name for a type of manta ray: In his Cumorah Revisited (1910), Charles A Shook reports (p 493) that ?In the Saints? Herald of April 4, 1906, under the heading, ?For the Wisdom of Their Wise Men Shall Perish? (Isa. 29:14), appears an article on Book of Mormon names in American nomenclature,? which named ten places, including Manti, as ?Lately Found? by explorers. (Note that the Saints? Herald is RLDS). Shook goes on to specify (p 495) that ?The name Manti Mormons have found in the American Antiquarian, Vol. XXII., No. 2, March and April, 1900, p. 129, in the account of the finding of certain archæological remains in Ecuador,? but, Shook argues (p 496), the spelling is ?Manta? rather than ?Manti? and that it ?is not an original American name at all, but is of Spanish derivation, meaning? an enormous devil-fish or sea-devil, an eagle-ray of the family Ceratopteridoe.? There was also ?a tribe of Indians called Mantas who lived in this locality.? Charles Augustus Shook, Cumorah Revisited: or, ?The Book of Mormon? and the Claims of the Mormons Re-examined from the Viewpoint of American Archaeology and Ethnology (Cincinnati: The Standard Publishing Co, 1910), 493-496.
B. Ammonites are an extinct type of shelled cephalopod: In 2013, Caitlín R Kiernan wrote a character that connected ammonites (shelled cephalopods) with the Ammonites of the Book of Mormon, among other cultural referents. Caitlín R Kiernan, ?The Ammonite Violin (Murder Ballad No. 4),? in Ellen Datlow, ed, Hauntings (San Francisco: Tachyon Publications, 2013).
C. The chambered nautilus is a type of Cephalopod whose shell forms a nearly equiangular spiral: A paragraph (1898) discussing the power of mental suggestion mentions ?the success of Joseph Smith, the first prophet of Mormonism, in certain of his attempts at healing.? The concluding sentence is: ?Beyond all question, the human soul is a chambered nautilus, building, to some extent, at least, its own shell.? WP McCorkle, ?The New Scientific Religion,? The Presbyterian Quarterly 12:45 (1898 Jul): 360 (344-377).