Green’s Dictionary of Slang

(US) to dance energetically.

1855		Thackeray Newcomes II 86: How the young Marquis was a cuttin’ of it about there! The pleace was obliged to come up and stop him dancing.
1920		‘The Cowboy’s Dance Song’ in J.A. Lomax Songs of the Cattle Trail 69: I fetched a cowboy whoop and started in to rag, / And cut her with my trotters till the floor began to sag.
1996		(con. 1944) G. Pelecanos Big Blowdown (1999) 32: He saw Tommy Rados cutting it on the dance floor at the Casino Royal.
1999		K. Sampson Powder 28: The one couple who could really cut it, dancing like they’d grown up in Havana rather than Hampshire, was Guy and Ticky.