According to the demand of space debris removal in the geostationary orbit, the dynamics and control simulation on the process of space debris tugged by flexible spacecraft was studied. The system topology configuration was analyzed, and based on the recursive method, the flexible mutibody system dynamics equations of service satellite and space debris were established, and the J2 perturbation of earth was considered. The cable dynamic model based on the lumped parameter method was also established. The service satellite and space debris were connected through constraint equations. And the attitude control torque of service satellite was calculated by the PD controller. Finally, the flexible multibody system equations of the process ware formulated. The cable model used in this paper was validated through the comparison between the catenary model and the lumped parameter model. The process of the debris tugged by the service satellite was analyzed through numerical simulation, in which the mass of space debris is near to the service satellite mass. Additionally, the corresponding dynamic property was studied, which can give some suggestions on the mission design of service satellite and the strategy of debris removal.