Snapping turtles are typically euthanized at shelters because of the lack of homes.
If the animal came from the wild and can take care of itself, it should be released back into the wild.
If he has been in captivity for a while, he will need to go to a refuge or a sanctuary.
You should check with the museums in your area and see if they are interested in him. You might also want to contact a wildlife cordinator in your area.
Let me know if you still have questions.