One version that aired on television omitted the entire subplot of Vinny making a deal with a pool player, and the scene where Vinny finds out there is a slaughterhouse next to one motel they stay in. References that Vinny makes to both these elements are cut out from his rant to Lisa about all the trouble he's going through for his court case.
During the filming of the movie, an alternate version of the film was shot for television viewing. It omits all cursing not by bleeping or covering the words, but the actors themselves shortening or changing their lines. This version is usually seen on Fox Networks.
The Australian TV version cuts out several lines of dialogue and the scene "Imagine you're a deer...." to get a PG rating. The video and cable versions are unaltered.