The space manipulators operate in an unstructured or unknown environment, increasing the dynamic complexity of space manipulator. Due to disturbance in manipulator base, the trajectory tracking control issue arises that cause error between reference and actual trajectory. Hence, to sort out these issues, this work presents optimum joint and trajectory tracking control of multi-axes space manipulator based on amnesia feedback controller. Firstly, the dynamic model of a 7DOF space manipulator built on Euler-Lagrange theorem, using the Jacobian matrix of individual link is designed. Later on, the Amnesia controller strategy is implemented that keeps a record of the trajectory tracking error and sends them to the robot tip. Compared to PID control scheme, the rising time, settling time, and overshoot is reduced even further when amnesia controller is used. The trajectory deviation using PID controller is 15°, while it is 3° using Amnesia controller, as expected. Hence, Amnesia controller reduces the trajectory tracking error between reference and actual trajectory of the redundant robot. The effectiveness of the proposed methodology employing a redundant 7DOF space robot has been verified. This proposed scheme can be utilized for on-orbit servicing and space debris removal through space craft.