You might not be able to make an alligator let go if it’s chomping on your arm.
An alligator’s jaws are extremely strong and once it bites down, it’s a real pain to get it to let go.
The opposite is true and when the alligator’s jaws are closed, it takes relatively little power to keep it shut.
Your best bet if you have a gator hanging off your arm or leg is a hard punch to the sensitive snout area, or a poke in the eye.
Good luck!