I am not going to pay a mechanic who partially fixed my car
What do you mean by partially fixed?
After I left the mechanic, the car stopped working
The correct thing to do is to go back to the mechanic and let him know that the car is not working. If you do not bring the car back to him, then he does not know that the car is not working. The mechanic can sue you for the money if you do not pay him.
I did go back and he didn't do anything, I want a refund!
If the damages are a lot of money you can take him to small claims court. There you will be able to get back the money you paid for the car that was not repaired properly.