Stuttering is a very sensitive issue which needs to be handled with compassion. The stigma attached to stuttering is tremendous in our society.
People with faltering speech disorder faces humiliation while in public speaking. Sometimes these people fight their deficiency. Whilst most of the time it remains suppressed within themselves.
In the occupation of stand-up, clarity in speech is pivotal. If your words are not clear for the audiences, your splendor goes ignored. No matter how good your jokes are, proper delivery is essential.
What would happen if you are a stand-up comic but you stutter? This Nescafe video explains it well too clearly. Your respect for people speech problems will increase tremendously.