The song contains spoken word portions (as the voice of Tommy the Cat) interspersed with the singing of Les Claypool. In their live performances Claypool does both parts himself, but singer Tom Waits provided the voice of Tommy the Cat on the studio version from Sailing the Seas of Cheese . The song features a complex slapping bass line by Les Claypool.
Primus released "Tommy the Cat" following their first major label single, "Jerry Was a Race Car Driver". In concert, Claypool started introducing all of their other songs by saying "This next song is not Tommy the Cat", apparently due to the popularity the song had gained after a video was released and played on MTV. 
The song was briefly featured in the 1991 film Bill and Ted's Bogus Journey during the 'Battle of the Bands' portion of the movie, where Primus was shown performing it.