The space sector is currently undergoing a push from the industry, several governments, and academia to enable routine satellite servicing in orbit. Among the many challenges, the complex dynamic interactions between the satellite base and the robotic arm are of primary concern. Although some missions may rely on the grappling of the host satellite, which would simplify servicing by virtue of fixing the relative kinematics between the two satellites, future space missions may also require a single point of contact between two satellites. Thus, precise end-effector control of the maneuvering satellite and its base is required. Although effective control tools exist in the fields of spacecraft pose control and robotics, simple methods to combine them are lacking in the space robotic servicing literature, which often requires complex derivations and can be subject to constraints, as is the case with a fixed center of mass or a zero angular momentum system. In this paper, the well-known recursive Newton–Euler approach is combined with appropriate spacecraft control algorithms to perform coordinated control of a spacecraft manipulator system. The interface between the two models is discussed (the base and the manipulator), and several realistic actuation models are incorporated, including thrusters and momentum exchange devices. In addition, a novel actuation approach through a cluster of four variable-speed control moment gyroscopes is proposed. The system is simulated and the proposed controllers implemented and tested according to the different actuation modes of the spacecraft. The simulation results are discussed, and the performance during each scenario is analyzed.