edThe best way to rid yourself of a monkey from your shoulder in Ark is to make it unconscious. First, ensure your character is at full health and well fed.
Then, approach the monkey with caution and aim your slingshot directly at it. Fire a stone at the animal until it is unconscious. Then, use whatever item is necessary to pick up the monkey and carry it away from you.
Once the monkey is at a safe distance, it will awaken and run away.