Please, *please* don't let a stutter prevent you from doing anything. I know first-hand how tough this exact decision can be, but please remember that you are a role model and a champion for all of us who stutter. Shying away from something is usually not the optimal course of action. A little more than 10 years ago, deciding to TA was one of the best choices I made as it made me master the material (which helped later for my professional examinations) and helped with confidence speaking. While I stuttered a bit in the tutorial sessions, I struggled mightily with the office hours answering student questions. Maybe this was due to the fact that I could prepare in advance for what I was presenting in the tutorials, but being put on the spot and with often a line of impatient students chatting and on phones was really stressful at first (it was so bad at first that I asked my GF to come and study during the office hours to give me some support). It got better by the week and I eventually TAed a couple other sessions. Someone once told me something along the lines of *"if the world thinks you have something important to say, it will listen patiently and carefully"*. You know the material well and that's the hardest part. Plan ahead as much as you can, don't expect to be perfectly fluent (few people ever are), and remember that most of the students aren't paying close attention and in my experience, I had many professors who were brilliant, yet English was their second or third language and had different troubles communicating. I knew that, eventually, I could help my students learn the concepts, stutter or no stutter. Why not give it a shot?