AYC, I can only imagine that you are talking about a real-world situation and not here in cyber space. I certainly hope that you would not walk away due to one dig from one person.
IMHO, when a hurt is fresh and new we are extra emotional about it and are thoughts and feelings are a bit overblown. WE will “never” speak to that person again, WE will never go out of our way for anyone again, WE will never step foot in that person’s home again, WE will never forgive …. That is why we are constantly reminded “never to say never”.
I believe that you need a little time to get over the initial shock and pain of the affront and then understand your own worth and value. No YOU should not step away from the group. To do so would NOT be beneficial to anyone, it would be a blow to your self-esteem and self-confidence. We can manage to agree or disagree with others, and we can learn to take a hit now and then. But basically we need to learn to all play nice in the sandbox.
If this person continues to attack you, IMHO you should confront it head on and simply ask “do you have a problem with me? I don’t appreciate your digs, they aren’t funny. So if you can’t be civil, lets just agree not to speak.” Whoever it is might be a sarcastic person by nature and no one ever called them on it. Then if you find yourself together with that person in a group. Try to feel as comfortable as you can. If you are addressed directly simply say “I don’t choose to debate this with you personally” and keep it as civilized as possible. Then either wait for someone else to speak or start speaking to someone else. But remember from YOUR part don’t invite discussion by commenting on what the other person is saying. Speak only about other people’s comments.
How does that sound, is that something you can be comfortable with?