Hi! I am a man about 28 years old. I am a stutterer,so I am looking for a speech therapist. Whoever knows speech therapist doctor, please tell me. I live in Riyadh; therefore, I am interested in someone who is in Riyadh.

Contact a hospital in Riyadh, and ask for the stroke unit. Or go visit in person.
They have speech therapists and one is probably trained to help with stuttering. You don't need a 'doctor' as in MD.
Watch the movie The King's Speech for ideas on your own, if you haven't already.