Jimmy Valmer from South Park was portrayed as a character with handicap and stutter but I don’t remember him being mocked or being a dum-dum. He’s rather a nice, rational guy on the show, accepted by his friends. But one of the best impressions of a stutter I have even seen in a movie was by Austing Pendleton in a movie “My cousin Vinny”, portraying a lawyer in a courtroom. It is both funny and so emotional for me to watch the scene as it is sooo real. Later I read the actor actually stutters (but not while acting) so he knew exactly what to do.