Which movie had a pet turtle with gemstones on its back?

The movie you're thinking of is "Teenage Mutant Ninja Turtles" (1990). The pet turtle, named Splinter, had gemstones on his back, which were actually shards of a meteorite that gave the turtles their mutant powers.

While the movie is about the turtles, Splinter plays a significant role as their wise mentor and father figure.