Gracie was a terrible biter when she was a puppy. She was playing of course but those little teeth are sharp. We also had a litter of kittens I had taken in at the time and she loved to wrestle and play with them. That would get her in full terrier mode and it would be hard to calm her down. The little stinker would actually roll on her back and bare her teeth at me!
I found that I had to refuse to play with her. As someone said "time out" is in order. Either get up and ignore or put in another room or cage for a short time.
Everyone wants to play with a puppy but when it gets them to the bite stage it is time to back off. I had to keep Gracie calm. Instead of excited play encourage calm petting and training sessions. I did not let anyone play tug games or anything that would get her excited. She did learn but it took time and being consistent with the rules. Playing typical puppy games will only encourage the biting.