There are likely many factors involved (outside of specifically diagnosed cases). Ask yourself this: What would it mean for stutter to be exclusively psychological or exclusively neurological? If the former, I'm sure you'll agree that this thing we call "brain" is involved in that. If the latter, I'm sure you'll agree that this thing we call "behavior" is involved in that. Basically, there's no clear cut between those two areas in a situation such as ours. We might start thinking about stutter in terms of something happening to the organism (in its environment) instead. - As for the rest of your post, I think it's important that we use a better developed concept of what communication is. It's not just "building sentences in your head" and "delivering words through your mouth". Language is something we perform, whether covertly or overtly, and those two modes are not automatically or mechanically linked. When we think of something, we enact it to ourselves. When we speak something, we enact it to ourselves and/or to someone else. It's a performance each and every time. - Stutter can vary a lot, depending on what we do. That's because communication is never just a simple case of transferring words from one place to another. It's different kinds of performances, involving different parts of our abilities, and is influenced by different things throughout (and sometimes _not_ influenced, as the variance would have it).