I'm not sure if will help everyone, but taking more controlled breaths into my stomach rather than my chest has helped me with breathing. I also find that talking slower and pausing more to take breaths has helped. I know people hate the "slow down" advice but it can help in controlling your speech and making it easier since stutters usually also are physically less able to articulate as quickly. Obviously breathing problems from stuttering come from you trying too hard to make a sound and getting out of breath in struggle.