According to the WiseGeek website: Some theorists believe that dancers could be said to cut a rug when they danced so well and so regularly that they would have worn out a carpet. In some regions, a particularly skilled dancer is said to “cut a mean rug,” a nod to the notable abilities of said dancer. In addition to being charming, this explanation is highly probable. Carpets are known to show extensive wear with small slits which could resemble cuts, and the link between heavy dancing and wearing out the floors seems obvious.

Other theorists have suggested that the term is related to rugs in the sense of taking them up or moving them. When a spontaneous dance party arises, rugs and furniture are usually moved out of the way to facilitate dancing. Rugs could also be removed in the long term to create a dance space, as would have been common in the 1920s, when Prohibition caused many social clubs to go underground into private homes. While the rugs might not have been literally cut, they could have been moved to safekeeping to avoid damage from dancing.

Whatever the origins of the idea of dancing enough to cut a rug may be, the term is charmingly descriptive. The 1920s was an era in which more vigorous dances began to be popular, and the idea that young people were dancing so robustly that the carpets were in danger may have been held by more traditionalist dancers. As often happens with disparaging comments made by outsiders, “cut a rug” may have been picked up by the exuberant dancers to describe their activities. One will note that modern and jazz dances can be said to cut a rug, while traditional minuets and waltzes are usually not associated with the colorful expression.

One responder to this article noted Cutting a Rug comes from Square Dancing and was performed by cowboys with spurs on. The repeated patterns of Square dancing and the wear of the spurs on the rug would “cut” it.