Green’s Dictionary of Slang

half-cut adj.1

[SE half-cut quality, those who look down on everyone other than those who look down on them]

(US) crude, uncultivated.

[US]Wkly Rake (NY) 1 Oct. n.p.: Frequented by half-cut swells, gentlemen ‘what live by their wits,’ ‘coves what have seen better days’ [etc].
[US]R. Carlton New Purchase II 254: Horse-pistols were sought and fixed [...] since there were half-cut backwoodsmen enough, and some degenerate natives to use them.

In phrases

do it in the half-cut (v.)

to give oneself airs, to show off.

[UK]Crim.-Con. Gaz. 6 Apr. 113/1: If I ever catch him doing it in the half cut again, I shall tell Miss Jones of the sly game he is carrying on.