Reproducing the orbit–attitude–vibration coupling dynamic behaviors of the complex flexible spatial structure provides the basis on the orbit design, the attitude adjustment and the vibration control of the structure. In this paper, the tug–tether–debris system is simplified as a spatial particle–spring–beam physical model, in which, the non-smooth stiffness coefficient of the spring is assumed to describe the tension/loose state switching of the tether. Based on the variational principle, the coupling dynamic equations are deduced for the spatial particle–spring–beam model. To investigate the energy evolution and the energy transfer characteristics of the model, the structure-preserving iteration method is developed focusing on the non-smooth stiffness coefficient of the spring. In the structure-preserving iteration method, the symplectic Runge–Kutta method is employed to solve the ordinary differential equations mainly controlling the plane motion of the system and the multi-symplectic method is employed to solve the transverse vibration of the beam in the model. The structure-preserving characteristics of the iteration method result from the symplectic structure contained in the symplectic Runge–Kutta method and the multi-symplectic structure contained in the multi-symplectic method. In the stages when the spring is in a complete loose or a complete tension state, the total energy of system is a conservative quantity that is preserved by the structure- preserving iteration method in the simulation. In addition, the energy transfer laws of the system in the tension process of the spring are revealed numerically, which gives some guidance on the active flexible space debris removal strategy design directly.