No, don't take him out of school. He isn't being bad or naughty; you are not failing.
Oddly enough, DS2 (the biter) is popular, despite his lack of speech and the perfect round bite-marks every single one of his class had from him last year.
Yes, some parents react very strongly to a bite but realistically, most kids try out some anti-social behaviour: pushing, punching, biting, swearing, hitting, pinching or excluding. Just most are not so obvious.
Interestingly, the only parents who were really supportive had kids who struggled with something.
Is he open to bribery? Does he get the concept? I tried it with DS2 to no avail but mercenary DS1 loved it . If he is, start the day with "No biting at school and we will ..... (reward - time at the park, softplay, sweets, tv).
Is there any pattern to the biting? Tiredness, hunger, time of the day? DS2 was a random-biter - it covered all eventualities.
DS2 got bitten but that didn't stop him. The nursery didn't cope with him and I did remove him from there but school just ploughed on and so far in class this year so good. The last couple of times have been at soft-play so I have removed him.
Keep going. You don't bite at home. This is not learnt behaviour. You are not to blame - so, treat yourself, too. It will stop - it is getting better and point this out to other parents, too. Big apology first, short explanation and that you are doing everything you can and it is getting better.