This paper presents a collision-free detumbling strategy (CFDS) for a space manipulator to detumble a non-cooperative target while avoiding collisions in a static or dynamic environment. The joints’ acceleration limits as well as the dynamic uncertainties of manipulator and target are taken into account. This strategy is comprised of a detumbling velocity trajectory generator and a trajectory tracking control scheme. An acceleration potential field (AccPF) method is proposed to plan the detumbling velocity trajectory, whose attractive potential field eliminates the initial momentum while the repulsive one forces the manipulator away from obstacles. Besides, an RBF neural network (RBFNN) adaptive control scheme is established to track the planned detumbling velocity trajectory while keeping the attitude of the base unchanged. What’s more, the stability of this control scheme is validated by a defined Lyapunov function. Several simulations were carried out, and the results validate the effectiveness of the CFDS.