Paul Brocklehurst, a speech and language researcher and Director of the Stammering Self Empowerment Programme, has written an excellent introduction to mindfulness and stuttering.
You can find it here.
I really like the emphasis he puts on mindfulness not being about relaxation. It’s about working with what you have at any given moment, and that might just as well be anxiety or tension as calmness. There’s also a really interesting account of the author’s own experiences of mindfulness/meditation and how these affected his speech.
Mindful Stuttering 