Can I legally stop payment on a check for new car purchase due to a defective transmission?

If you bought the car without a warranty, you've got trouble here.  This isn't a "new" car except to you, and I suspect that you didn't buy it from a dealer.  As far as the law is concerned, you had to have understood that you bought this clunker "as is," and its problems are now your problems.  You should talk to a lawyer as soon as possible, and I'd recommend doing that before you try stopping payment on the check.

If there's no warranty on a used car, or even if there is, give serious consideration to having it looked over by your own mechanic, before you sign the contract or pay for the car.  If the seller isn't willing to let you do that, walk away.