The control problems of a flexible-base and flexible-joint space manipulator with uncertainties were addressed, and a mixed control scheme was proposed based on adaptive robust terminal sliding mode control and adaptive optimal vibration control. Firstly, the system was reduced to a slow subsystem and a fast subsystem by singular perturbation method. Secondly, a trajectory-tracking adaptive robust terminal sliding mode control scheme, including an equivalent control, a robust control, and an adaptive adjusting algorithm, was presented for the slow subsystems. And then, a vibration optimal control strategy was proposed based on adaptive state observation for the fast subsystems. The simulation results show the validity of the proposed scheme in rigid and flexible motion controls of the system.