My son is 7 and this story sounds very similar to mine. I recommend finding an SLP who knows how to handle stuttering. My son has been receiving speech therapy for about 6 months and has made amazing improvements. He went from a severe stutter to it a mild stutter. He actually has two therapists one works on the emotional side of things teaching him how to be confident despite the stutter and the other teaches him techniques to use when speaking to minimize the stutter. It seriously has been life changing for him. It is so hard since all of the parent recommendations are about not drawing attention to the stutter. But I guarantee that your son is aware of it and his classmates are aware of it. It's better to get in front of this before he really starts feeling bad about it. Good therapy is amazing.