Quizlet doesn't currently let you clear high scores or "completed learn mode." However, there's a quick solution if you want to re-use a set for a new class or school year.
Just make a copy of your own set. It take seconds and will have no high scores or completed learn mode. You're still the creator of the set with editing privileges but you'll have to reset your privacy settings on the set.
You can delete the original to prevent confusion.