It's so important to notify HR people before your interview that you have a stutter. Whenever I have a meeting with someone new, I always let them know I have a stutter when I accept the invitation. This simple thing reduces my stress (which means I'll likely be more self-confident) and professionally lets the company make allowances for your situation. I'm sorry you had this experience but for your next interview, let them know you have a stutter before you arrive.