Stumpy and Olaf are usually not on very good terms with each other.
Stumpy makes fun of Olaf for a variety of reasons, the most common one being that he is short (though ironically, Stumpy himself is the second shortest in the cast). Like his friends, Stumpy rarely takes Olaf seriously. In "Let's Play Frosted Christmas - Part 2", Stumpy gets angry at Olaf for kidnapping Kaeloo, Quack Quack and Mr. Cat, and after rescuing them he destroys the igloo even though Olaf desperately tries to stop him. To Olaf's surprise, Stumpy and the others simply walk away after defeating him.
Olaf seems to dislike Stumpy and the rest of the main four. He finds the squirrel to be annoying and stupid. In "Let's Play Stumpy's I.Q.", after Stumpy becomes a genius and tries to create a bomb, Olaf tries to force him to give him the bomb so he can take over the world, which Stumpy refuses to do because he also wants to tale over the world. At the end of the episode, however, they find out that they are both fans of Jimi Hendrix, and they do air guitar to his music together.