Green’s Dictionary of Slang

cut adj.¹

drunk; thus half-cut adj.² (1)

1650		implied in cut in the back under cut v.2 .
1652		Mercurius Democritus 27 Oct. - 3 Nov. 235: Bench-whister to all Skinkers, Lick-thimbles, Down-right Drunkards, Petty Drunkards, Roaring Boys, Swaggerers, Pot and Half-Pot men, Short-winded Glass-men, Master of the Horse called cut.
1663		J. Wilson Cheats V v: How pitifully my husband is cut! He’ll be so sick to-morrow morning.
c.1698		B.E. Dict. Canting Crew.
1746		W. Dunkin Parson’s Revels (2010) 71: True Cocks, though cut, we clap and crow, / The more we drink, the dryer grow.
1770		Gent.’s Mag. Dec. 559/2: To express the condition of an Honest Fellow [...] under the Effects of good Fellowship, it is said that he is [...] 30. Cut.
1781		Poetical epistle from Florizel to Perdita n.p.: We did not carry off less than a dozen bottles each (!!!) and he was as sober as a Methodist parson. As to my part I own to you I was d****bly cut.
1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue n.p.: cut drunk; a little cut over the head, slightly intoxicated.
1799		Sporting Mag. Nov. XV 87/1: Found him, with a large party, all pretty much cut.
1803		‘A Pembrochian’ Gradus ad Cantabrigiam 52: to be cut; to be half seas over.
1811		Lex. Balatronicum.
1819		‘One of the Fancy’ Tom Crib’s Memorial to Congress 45: Old BILL, the Black [...] Though somewhat cut, just begged to say / He hop’d that Swell, Lord C-ST-R-GH, / Would show the Lily-Whites fair play.
1825		C.M. Westmacott Eng. Spy I 159: Most of the party were a little cut.
1833		T. Hood ‘Ode to Admiral Gambier’ Works (1862) II 431: Who would cut a man because he’s cut?
1837		N.Y. Dly Herald 24 May 2/2: Both parties were well cut — Silk with a knife and Erskine with liquor.
1842		Flash 14 Aug. n.p.: Awfully cut and half groggy.
1846		Bell’s Life in Sydney 20 June 3/2: Cutter declared that [...] while she was rather cut, she smashed the teapot in her tantrums, and they had to boil the beverage in the kettle.
1849		Thackeray Pendennis I 188: After a dinner at the Cafe de Paris, ‘when we were all devilishly cut, by Jove.’.
1856		C. Reade It Is Never Too Late to Mend II 279: When I’m a little cut you may know it by my quoting Shakespeare.
1860		Hotten Dict. of Modern Sl. etc. (2nd edn).
1874		‘Old Calabar’ Won in a Canter I 110: ‘All right, old fellow [...] I am cut a little; bottle of sodash water putsh all straight.
1890		Sporting Times 12 Apr. 1/5: A barber had a drinking bout / Neat brandy was his crave; / Next morn his ‘clients’ found him out, / He cut, but could not shave.
1921		N&Q 12 Ser. IX 346: Cut. Intoxicated.
1933		‘William Juniper’ True Drunkard’s Delight.
1963		C. Wood ‘Spare’ in Cockade (1965) I i: Everybody gets cut.
1972		A. Mitchell Half-gallon Quarter-acre Pavlova Paradise 182: cut: Drunk.
1992		Guardian 22 Feb. 31/4: Others [...] need a few bevvies before they can make conversation. Fine, so long as they’re only two-thirds cut.
1974		Star Press (Muncie, IN) 24 Oct. 23/2: The Irish have at least two dozen words for inebriation [...] killarneyed, fluthered, stotious, pallatic, maggoty, blithero, half-tore, paralytic and stoven.
2001		K. Waterhouse Soho 202: Guzzling whisky, he was already, so Alex judged, three parts cut.

In phrases

cut over the head (adj.)

tipsy, slightly drunk.

1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue.
1811		Lex. Balatronicum.
1821		R. Waln Hermit in America on Visit to Phila. 2nd series 27: ‘He’s a cunning shaver’ — ‘A little cut over the head’.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.