How do I pronounce the th sound in English without biting my tongue?

The bite is the problem, not the tongue. Rest the tip behind the top front teeth, or between the teeth without pressure, and send a thin stream of air over it. If the air stops and pops, the tip is pressing; release the pressure and the sound appears. Keep the jaw relaxed too, because a clenched jaw pulls the tongue back into a t.

If the biting habit is hard to drop, run the whisper test first. Whisper the voiceless words from the word list and listen for a soft hiss; a whisper removes the buzz, so anything that still sounds like a hard stop is a placement problem rather than a voicing problem. Then whisper the voiced examples and add voice only when the hiss is clean. If the tongue tip cannot sit between the teeth because of a brace, a crown or a missing front tooth, keep it just behind the upper teeth instead and let the air pass over it and out through the gap, which is the other position English speakers use for the same sound. One more correction: cut the repetitions. Five slow, accurate words are worth more than fifty fast ones, because speed is what brings the stop back.

The Two 'th' Sounds in English: Tongue, Word Lists and a Self-Test →