I think the chances of you earning an FAA 3rd class medical certificate are good, even if your stuttering is moderate.
Severe stuttering, I don't know.
I personally don't know any stuttering pilots, but I know two commercial pilots who have mild Tourette's.
My advice is talk your personal doctor first, then see an Aviation Medical Examiner in person, just for a consultation. It might cost you $100 US, but it would be worth it for their opinion.
Pilots start out here in the US often without speaking much English at all, so stuttering is not that bad. Check in with those doctors.
Best of luck!!