If your stutter is that bad, begin the interview with letting them know you have a stutter. Be like, "thanks for taking the time to interview me, before we begin I just wanted to let you know I do have a stutter however it has not prevented me from being successful at work or school in the past and I promise it wont affect me in this poition if I was fortunate enough to be accepted". After you say that, I promise you the tension will be much less and you may even stutter less. I have said the above in a job interview and also received the job, for a technical support call center role