Are you in the US? This could be ground for a discrimination case per the ADA, especially since the reason they gave was that you were slow speaking. Only an idiot from HR would say that, they should have just said that they were no longer considering you as a candidate and left it at that. Lawyers have told me that "refusal to hire" cases are very difficult to win and many of them will not take them, but if you were actually told that your stutter was the reason for not hiring you then that is a big red flag and I would suggest contacting a lawyer. I was lucky and got a job at a very understanding company. Even though I am expected to use the phone very often and am the front-line for customer service, they don't mind too much that I have a mild stutter.