If the frog is an adult there is no need to just feed worm pieces. Feed whole worms and it will be less likely to bite the tongs. Now it will still happen occasionally so when it does just gently wiggle them out of the frogs mouth. With a frog that bites the tongs often you're going to want to buy rubber tipped tongs so the frog doesn't harm its jaws.
Some nightcrawlers are just to huge, I didn't know if it would be okay to give a whole one to them, so I was cutting them in half and he still gets really anxious. He's just a pig.