What's the noun for stut? Here's the word you're looking for.
stuttering
A speech disorder in which the flow of speech is disrupted by involuntary repetitions and prolongations of sounds, syllables, words or phrases, and by involuntary silent pauses or blocks in which the stutterer is unable to produce sounds.
“Possibly stutterers may be shy or hostile because of developmental origins at an oral dependent-incorporative level.”
“But I know a number of stutterers now who I feel very sorry for, because I can see how inhibiting it is for them, and how crippling.”
“They found that a portion of Wernicke's area, which is believed to control language comprehension and auditory processing, was significantly enlarged in stutterers.”