Any and all of Kundalini Yoga can be helpful with stuttering. Kundalini Yoga balances and coordinates the areas of the brain and reduces stress, and helps the part of the brain connected with speech to send more effective signals to the nervous system.

We recommend the Journey Through the Chakras DVD, especially the segments that work on the Navel Chakra and the Throat Chakra. The last exercise on the Throat Chakra segment is a meditation in which you say the mantra Sat Nam (6x) - Wah Hay Guru (1x), twice per breath.

Arms are extended up to 60 degrees in front of you, thumbs hooked. Eyes are 1/10th open and looking down and in, towards the tip of the nose. Try to work this one up to 11 minutes a day. To end, inhale and stretch your arms straight up, shake your arms, then relax the breath, lower
the arms, and sit in silence for a minute.

We also recommend the Sa Ta Na Ma Meditation on Yoga Quick fixes, and Yoga House Call. Also, any and all of the chanting in Kundalini Yoga will be helpful.

When you talk to people imagine that you are singing your words.

from the Mayo Clinic:

Researchers don't know the causes of stuttering, but factors that may cause stuttering include:
• Genetics. The fact that stuttering tends to run in families suggests
there may be an underlying genetic cause.
• Language development. Stuttering affects many children as they learn to speak (developmental stuttering). Young children may stutter when their speech and language abilities aren't developed enough to keep up with what they want to say. Most children outgrow developmental stuttering, often within four years.
• Signal difficulties. Stuttering may occur because the signals between a person's brain and the nerves and muscles that control speech aren't working properly (neurogenic stuttering). This type of stuttering can occur in children, but it also may affect people who have had a stroke or other brain injury. Rarely, neurogenic stuttering may be the result of structural abnormalities (lesions) in the motor speech area of the brain.

Stuttering often gets worse when you're excited, tired or under stress, or when you feel self-conscious, hurried or pressured. Speaking in front of a group or talking on the telephone can be particularly difficult.

Although it's not clear why, most people who stutter can speak without stuttering when they talk to themselves and when they sing or speak in
unison with someone else.

from neurology:

What causes stuttering?
Although the exact cause of stuttering is not known, there are three leading theories that propose how stuttering develops. The learning theory proposes that stuttering is a learned behavior and that most normal children are ccasionally disfluent (i.e. speaking rapidly,searching for the right words, etc.) when at the age at which speech
and language develop. If a child is criticized or punished for this, he or she may develop anxiety about the disfluencies, causing increased stuttering and increased anxiety.

The second theory suggests that stuttering is a psychological problem-that stuttering is an underlying problem that can be treated with psychotherapy

The third theory proposes that the cause of stuttering is organic, that neurological differences exist between the brains of those who stutter and those who don't. Although the interference with speech is sometimes triggered by emotional or situational factors, stuttering is
basically neurological and physiological – not psychological - in nature. In all other respects, persons who stutter are perfectly normal.

There is also some indication that genetic factors are involved in the development of stuttering and subsequent recovery, as shown by various studies done on families and twins. It is not known to what degree stuttering is dependent on genetic factors, on environmental factors, or on both. The most common type of stuttering (sometimes called developmental stuttering) usually develops of its own accord in childhood, most often between ages two and eight (although in rare cases it may begin much later). Roughly 4 to 5 per cent of people experience stuttering at some time during their childhood. While the majority become fluent by the time they reach adulthood, stuttering may continue to be a chronic, persistent problem for other stutterers. In short, stuttering is thought to be a physical disorder and is not thought to be caused by psychological factors such as nervousness or stress, or parenting practices or the way parents communicate with their children when they are young.

Stuttering tends to run in families, and it is generally accepted that this is because genetics is involved in the cause. However, the precise nature of the inheritance is unknown at present. Because stuttering occurs in families, speech researchers are inclined to say that stuttering has genetic roots. Recent advances in the field of human genetics allow scientists to identify the genes that cause any disorder which shows inheritance in families. The identification of "stuttering genes" is the subject of The Stuttering Family Research Project at the National Institutes of Health, a project which has identified over 350 families who can donate cheek samples to be analyzed for DNA. There is a small but growing pool of data which show that the brain shows certain focal abnormalities in persons who stutter. These abnormalities appear only when the individual is speaking and appear within the premotor, motor, and auditory association areas of the cerebral cortex. Neuropharmacological attempts to control stuttering have been developed, but side effects of such medications have been numerous and unpleasant.