A clutch control device and a clutch control method are capable of preventing progress of wear and damage of a pneumatic clutch actuator. The clutch control device that controls the operation of a pneumatic clutch actuator to disconnect a clutch is characterized by setting a stroke amount of a piston corresponding to a disconnection position of the clutch as a final target stroke amount, setting other stroke amounts different from the final target stroke amount as intermediate target stroke amounts, and controlling the operation of the piston in a stepwise manner such that an actual stroke amount of the piston is matched with the intermediate target stroke amounts and is thereafter matched with the final target stroke amount, thereby disconnecting the clutch.