Green’s Dictionary of Slang

to dance (cf. rug cut v.); thus rug-cutting n., dancing.

1936		Lil Johnson ‘Rug Cutter’s Function’ 🎵 Get all high and cut some rug!
1942		‘Marienne’ ‘Solid Meddlin’’ in People’s Voice (NY) 9 May 31/2: [They] put the finishing touches on their birthday frolic [...] by cutting a rug or two.
1944		D. Burley Orig. Hbk of Harlem Jive 28: The cats grabbed the chippies, and St. Mick forgot, / And began some rug cutting, to music most hot. [...] Then he copped a quick trot to the smoke-hole once more, / As the Cats and the Chippies cut rug to the floor.
1954		Hepster’s Dict. 1: Beat the rug – Dance.
1965		F. Pollini Glover 88: She’s having a grand time! Out there cutting the rug with ol redbeard.
1978		R. De Christoforo Grease 30: Com’mon, let’s cut a rug!
1980		Eble Campus Sl. Fall 2: cut the rug – dance.
1989		R.E. Tangney Other Days Around Me 126: The more strenuous exertions of ‘cutting a rug’ at a local dance-hall.
1999		Guardian G2 30 Nov. 17: Almost certainly not cutting a rug at the subsequent aftershow knees-up.
2008		T. Dorsey Atomic Lobster 151: They could cut a rug with the best [...] the tango, the rhumba, the watusi.
2012		(con. 1943) G.S. Manson Coorparoo Blues [ebook] He was no musical dunce: he could still cut a rug.