Drunk. A little cut over the head; slightly intoxicated. To cut; to leave a person or company. To cut up well; to die rich.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
See also the definition in Nathan Bailey's 1721 dictionary of canting and thieving slang.
custom-house goods * to cutNathan Bailey's 1721 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes