The word stuttering is not found in the Bible. But at the burning bush, Moses told God he had a speech problem. Exodus 4:10-12, when Moses said unto the LORD, “O my Lord, I [am] not eloquent… I [am] slow of speech; and of a slow tongue….And the LORD said unto him….Now therefore go, and I will be with thy mouth, and teach thee what thou shall say.” Perhaps his speech was slow due to stuttering; we just don't know...
Science explains stuttering as a clinical speech disorder with prolongations of speech sounds, syllables or words, frequent repetitions, or the inability to start a word. Stuttering might be developmental, neurogenic, psychogenic, or even genetic. It can be successfully treated with speech-language therapy and education.
Many famous people have suffered from stuttering and were able to work through the problem. For example, Vice President Joseph Biden, Winston Churchill, Marilyn Monroe, Bruce Willis, Carly Simon, and Jimmy Stewart, all stuttered and learned how to talk without a trace of stuttering. None of these people reported demon possession.
Our bodies are imperfect. Sometimes people experience eye-twitching or facial grimacing, but these muscle-nerve issues are due to the Adamic fall, not to demons. Scriptural examples of demonic activity within a person include: fortune telling, severe self-mutilation, violent behavior, witchcraft and devil worship. The fruitage of demonic activity is always evil. The fruitage of stuttering is neither good nor evil. Stuttering is simply a sad, frustrating experience for the sufferer. Our response should be one of kindness, patience and helpfulness in order to treat the malady.
There is no evidence that any demonic influences are responsible.