Motivation is best viewed in terms of effort or cost for the client at any given point in his or her life versus the benefits expected or already achieved. There are some stutterers that we probably cannot treat. Natural speech with a little stuttering is a lot easier for the client and clinician to take than mechanical-sounding speech with no stuttering. I use what works. I typically opt for the most direct way to get the client to experience fluency.
Clients respond positively to straight talk and honesty.
Clients also respond well to humor. Emotions often do play a significant role in stuttering and, if so, need to be addressed in therapy. Have sufficient control over thoughts and feelings in order to modify their speech when necessary. Excellent clinicians for stutterers do not have to be stutterers themselves. There will always be more to learn.