The obsolete slang phrase to shoot the cat meant to vomit. [note 1]

The origin of this phrase is unclear. According to the English educationist and lexicographer Ebenezer Cobham Brewer (1810-1897) in Dictionary of Phrase and Fable, giving the Derivation, Source, or Origin of Common Phrases, Allusions, and Words that have a Tale to Tell (London: Cassell, Petter, and Galpin, [1870]), to shoot the cat alludes to the fact that cats are prone to vomit:

Sick as a cat. Cats are very subject to vomiting. Hence the vomit of a drunkard is called “a cat,” and the act of discarding it is called “shooting the cat.”

The earliest occurrences of the phrase to shoot the cat that I have found are as follows, in chronological order:

1-: From A Classical Dictionary of the Vulgar Tongue (London: S. Hooper, 1785), by the English antiquary and lexicographer Francis Grose (1731-1791):

CAT, CATTING, SHOOTING THE CAT, to vomit from drunkenness.
[…]
SHOOT THE CAT, to vomit, from excess of liquor, called also catting.

2-: From Vollständiges Wörterbuch der Englischen Sprache für die Deutschen (Leipzig: Bey Johann Gottlob Immanuel Breitkopf, Sohn und Compagnie, 1793), an English-German dictionary by Johann Ebers (1742-1818):

to Cat, or shoot the Cat.

3-: From Observations on a tour through almost the whole of England, and a considerable part of Scotland, in a series of letters, addressed to a large number of intelligent and respectable Friends (London: Published by G. Goulding, John Walker, and at the Author’s Warehouse, [1801-02]), by the Engish actor, composer and author Charles Dibdin (bap. 1745-d. 1814):

There is a story […] of a thorough bred seaman, who was perfectly ignorant of a most common-place term. When persons are sick on salt water so as to induce vomiting, the action is ludicrously called by the sailors shooting the cat. Sailors all the world knows are addicted to superstition, and in particular, partly out of fear and partly out of awe, hold in great veneration a cat. This sailor I allude to had a cat to which he paid great attention. One of the passengers on a voyage being surprized with a most violent sickness, and all its consequences, Zounds, said one of the tars, that man has been shooting the cat. “Has he, by God,” said Jack, “Damme then if I don’t go and shoot him.”

4-: From A Complete Collection of English Proverbs. Also, the most celebrated Proverbs of the Scotch, Italian, French, Spanish, and other Languages. The whole methodically digested; and illustrated with Annotations, and proper Explications (London: Printed for George Cowie and Co., 1813), by the English author John Belfour (1768-1842) [note 2]:

Proverbial Phrases and Sentences belonging to Drink and Drinking.

Lick your dish. Wind up your bottom. Play off your dust. Hold up your dagger hand. Make a pearl on your nail. To bang the pitcher. There’s no deceit in a brimmer. Sup, Simon, the best is at the bottom. Ale that would make a cat to speak. Fill what you will, and drink what you fill. She’s not a good housewife that will not wind up her bottom, i.e. take off her drink. He has shot the cat.

5?-: There seems to be a punning use of the phrase in the following passage from the “account of an indictment by an Old Lady against a Gentleman for shooting her favourite Cat” (dated Old Bailey, 4^th September, George the first), published in The Morning Chronicle (London, England) of Wednesday 31^st August 1814:

The Defendant then said,
Gentlemen of the Jury—Although I am altogether unacquainted with the forms and proceedings of the law, yet thinking the occasion too trifling to engage the attention of the Court by Counsel, I resolved to speak for myself; and I shall begin by a short remark upon the pious wish with which the Prosecutrix concluded her examination. She hoped, forsooth, I was not sober when I did the act for which she seeks to punish me.—Charitable Christian!—Shocked at the commission of one crime, she wishes I had committed a greater; because she not only wishes I had been drunk, but drunk to that excess as to shoot a Cat; a thing very rare amongst Gentlemen.

Notes:

1 Likewise, in French, the obsolete verb renarder was slang for vomir, i.e., to vomit. This verb derives from the noun renard, denoting a fox.

The verb renarder is first recorded in Dictionnaire Flameng-Francoys (Antwerp: Jean Waesberge, 1576), a Flemish-French dictionary by Mathias Sasbout.

2 Belfour’s Collection of English Proverbs is a “revised, corrected, and augmented” edition of A Compleat Collection of English Proverbs; Also, the most celebrated Proverbs of the Scotch, Italian, French, Spanish, and other Languages. The Whole Methodically Digested and Illustrated with Annotations, and proper Explications (London: Printed for W. Otridge, S. Bladon, etc., 1768), by the English naturalist and theologian John Ray (1627-1705). The phrase to shoot the cat is absent from Ray’s Collection of English Proverbs; conversely, the phrase he has pissed out all he has against the walls, recorded in Ray’s Collection of English Proverbs, is absent from Belfour’s Collection of English Proverbs—this is the relevant passage from Ray’s Collection of English Proverbs:

Proverbial Phrases and Sentences belonging to drink and drinking.

Lick your dish. Wind up your bottom. Play off your dust. Hold up your dagger hand. Make a pearl on your nail. To bang the Pitcher. There’s no deceit in a brimmer. Sup Simon the best is at the bottom. Ale that would make a cat to speak. Fill what you will, and drink what you fill. He hath piss’d out all he hath against the walls. She’s not a good house-wife that will not wind up her bottom, i.e. take off her drink.