I'm thinking of underpaying my teenage tutor
Is there a reason you do not want to pay them the full amount?
I may not pay him on time or in full if he doesn't want to do anything for me
If you are not satisfied with the tutoring service that you are receiving, then you can certainly stop working with this tutor. However, you have agreed to pay someone by the hour for their time, and it is your responsibility to pay in full for what you have already received.
I'm going to stop him from coming and he's going to lose out on business
Just make sure that you pay him the right amount before letting him go. You should not underpay someone the amount that you agreed upon, for any reason.