If stammering or stuttering is related to anxiety or stress (or tension), yoga has potential to help the people who have this problem.
I came across the following research paper and found that the anxiety and perceptions about communication were improved, causing resultant improvement in stammering problem.
https://pdfs.semanticscholar.org/5069/ae37ddd7d3520b9f727c8f49d9f589b764da.pdf
There are two types of autonomic nervous system :one of them is parasympathetic nervous system which is responsible for relaxation response, decreasing blood pressure and heart rate; and activation of limbic regions of the brain) and another one sympathetic nervous system activation which is responsible for the stress response including the release of cortisol and epinephrine.
Doing yoga practice – postures, pranayama and meditation - suppresses the sympathetic nervous system and activates parasympathetic nervous system. By doing persistent yoga practice, parasympathetic nervous remains dominant even during stressful situations. This keeps the people with stammering calm, increase confidence and in control of their speech. People with stammering doing yoga practice report relief from the tightness in chest, mind racing, anxiety and worry less about their speech.
1.You can practice the following yoga practice:
(i) Uccharana-sthala tatha vishudha chakra shuddhi kriya – this is the first exercise of yogic sukshama vyayama
(ii) Griva-sakti-vikasaka – this is the eleventh exercise of yogic sukshama vyayama (for more information, ask separately in related question)
(iii) Simhasana
(iv) Yogamudrasana
(v) Ujjayi Pranayama
(vi) Naada-Anusandhana Pranayama
(vii) Meditation on Vishuddhi Chakra (Bij Mantra Meditation – Lam, Vam, Ram, Yam, Ham, Om Chanting)
(viii) Yoga Nidra / Autogenic Training (with autosuggestion on improving speech)
2. Make a list of the words that you are feeling difficulty in speaking and check where you lag behind and make your exercise plan as per the articulation problem.
3. Rehearse reading loudly the contents of the newspaper in front of mirror with confidence.
4. Use Neurolinguistic Programming (NLP) to programme your mind for free flow of speech