Green’s Dictionary of Slang

cut, the n.

[SE cut, a passage; thus note The Cut, London SE1, one of 19C London’s best known street markets; also f. the knives wielded in such a place (Major, Juba to Jive: A Dict. of Afro-American Slang, 1994)]

(US black) the ghetto, the poor side of town.

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[US]C. Major Juba to Jive 125: [The] Cut n. (1990s) from ‘cut,’ as with a knife; a rough section of a city or town.