I would always recommend speaking in private because most people aren't aware that it's hurtful while they just laugh about it and fail to see it from any other perspective but looking at the extent of bullying, I wouldn't mind it if you risk disrupting the work atmosphere by standing up to her. I'm sure the person who stutters won't feel bad because as you already know, he has put up with a lot, so he won't view you standing up for him with embarrassment but will feel good about the support. So, in your situation, you don't have to worry about the feelings of both people and can choose any appropriate action.