I'm really sorry you're going through this. Having stuttering sucks at times, but it's one part of who you are, just like being gay. Mean people will be mean about everything. Try to be kinder to yourself and focus on the supportive and positive people around you at work. It’s best to stay polite and keep interactions with those negative people to a minimum. I recommend taking some time to think it over regarding HR, but in the meantime, start gathering your information, just in case you decide to file a complaint later on. Big hugs.