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Variation of "cut a rug" (i.e. 'to dance enthusiastically') - a term that became popular jargon in the 1920s.

The basis for the phrase comes from wear created by over-use of (by dancing on) an area of carpet.

Used in The Blutones' song 'Cut Some Rug' (You say I can talk to you anytime, Though I just wanna cut some rug).
This is a great song! Wanna get up and cut some rug?
by Wizzzzo October 04, 2010
To have sex.
Later tonight I think I'll pull Sharon back and cut some rug.
by Lust in a Can June 22, 2006
To have sex, as used by The Bluetones in the aptly named song 'Cut Some Rug.'
"You say I can talk to you anytime
But I just wanna cut some rug"
by sugar-spun-sister November 20, 2006