I stutter and I can tell you it has nothing to do with breathing. I had some untalented speech therapists in elementary school who would just tell me to work on slow breathing and to "stop and start over" when I reached a stutter. I knew even at a young age that it was a waste of time and effort. If you have to stop and start over each time you reach a block you're still disfluent. I'm more of an advocator of methods that get you through a stutter rather than around it, if that makes sense.