I'm not sure if this counts, since the characters weren't completely removed from the show, but nonetheless...
After the 1st season of Heathcliff and the Catillac Cats, Hector, Wordsworth and Mungo stopped appearing in the Heathcliff shorts, and were from then on relegated to only appearing in the Cats & Co. segments. Their roles in the Heathcliff shorts were taken over by a trio of previously unnamed alley cats who were later dubbed Lefty, Knuckles and Raoul. No explanation was given for the change, it just happened.
Also, Johnny Test's first crush, Janet Nelson, Jr., pulled a Houdini after the show's first season. Janet's only post-season 1 appearance was a non-speaking part as an extra in "Johnny Zombie Tea Party".