Green’s Dictionary of Slang

cut the rug v.

also beat the rug, cut a rug, cut rug

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

[US]Lil Johnson ‘Rug Cutter’s Function’ [lyrics] Get all high and cut some rug!
[US]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.
[US]Hepster’s Dict. 1: Beat the rug – Dance.
[UK]F. Pollini Glover 88: She’s having a grand time! Out there cutting the rug with ol redbeard.
[US]R. De Christoforo Grease 30: Com’mon, let’s cut a rug!
[US]Eble Campus Sl. Fall 2: cut the rug – dance.
[Ire]R.E. Tangney Other Days Around Me 126: The more strenuous exertions of ‘cutting a rug’ at a local dance-hall.
[UK]Guardian G2 30 Nov. 17: Almost certainly not cutting a rug at the subsequent aftershow knees-up.
[US] T. Dorsey Atomic Lobster 151: They could cut a rug with the best [...] the tango, the rhumba, the watusi.