The biggest problem of stuttering during interviews is not the stuttering itself, but rather the break in the train of thought while brainstorming answers to interview questions.
First off - phone interviews are a nightmare for me - and I almost always fail to make an impression - because of the several ticks I produce while trying not to stammer.
I used to think I would do better at face-to-face interviews, since I can at least write on the whiteboard. Every piece of interview advice I've read says that one should keep speaking while thinking during an interview, and not just be silent and think - which is how I work best, because my brain is freed from the burden of speaking correctly.
When I 'speak while thinking of solutions', my brain automatically starts focusing on being careful about not stammering, and that really hurts my ability to focus on solving the questions - which are quite difficult in the first place.
One solution that's partially helped: I know that many stutterers are much better off when saying something semi-rehearsed, whether it be a phrase like, "So the brute force solution is _____ " or whatever. My brain goes into mechanical mode while saying this phrase, giving it more time to actually think.
I've never revealed to interviewers that I have a stutter (even though they would probably suspect that by the end of the interview), but I guess you should consider what edw519 says in the top comment.
Please feel free to contact me if you have any other questions.