How do you destroy the rug at the mueseum on taz wanted the video game

I don't remember there being a rug in the museum level, however I think you might be referring to the wanted poster painted on the floor.  
To remove this poster you need to find the floor polisher which is located near the switch that controls the big lightbulb. Jump on the floor polisher and ride it all the way to the poster painted on the floor. Ride over the poster and it will be cleaned off and buffed up to a nice shine.