In the movie or in the series?
In the movie they did kick him out because he was planning on taking over the gang and because they got on his nerves.(I'm a big Scrappy fan, so I basically hated that part of the movie)
In the series, i'm guessing since he refered to Scooby as uncle Scooby then Scrappy lives with his mom or dad, and only visited Scooby and the gang every now and then.
I'm not sure if that's true or not, that's just what I think. But they sooooo need to bring Scrappy back. Come fanpoppers, let's petetion.