Green’s Dictionary of Slang

(US black) a friend, a close intimate.

1943		D. Burley N.Y. Amsterdam Star-News 3 July 16: My cutties, likewise draped in olive drab droops.
1964		R. Abrahams Deep Down In The Jungle 265: Cutting Man – Best friend.
1974		R.D. Abrahams ‘Black Talking on the Streets’ in Bauman & Sherzer Ethnography of Speaking 261: The larger term for this kind of play is cutting contest and, by extension, a friend with whom one can play, a cutting buddy, cutting man, or cutty.
1980		E. Folb Runnin’ Down Some Lines 35: There are a variety of other expressions that essentially carry the same sense of friendship and trust as ace: [...] cutty, cutting man.