It seems like your manager was being insensitive and intrusive. If I was in your situation i'd probably think they were crossing a line. But at the same time, I always inform potential employers about my stutter before the interview process so I can avoid this disastrous situation. Either way, it's not your fault and I definitely think you should talk to someone in HR about this. I don't know if I would file a complaint but I would inform them so maybe they can educate your manager on your behalf. Sorry you're going through this.