The science of stuttering isn't a done deal yet. Many factors seem to play in. There's also somewhat of a personal variance, I think, with regards to how stutterers perceive themselves and their impediment. As an aside, we should probably stop thinking in terms of "the mental or the physical" in general. It's not like there are two seperate realms like that, where we can sort everything we do neatly in one or the other camp. What we do is who we are, in a unified way.