The space-borne manipulator has been playing an important part in docking tasks. Docking collision can easily lead to instability of both the manipulator and floating base. Aiming at the problem of soft capture, a novel soft-contact joint with dual working modes is developed, especially to buffer and unload the spatial collision momentum. Furthermore, considering a series-wound soft-capture manipulator with multi-joints, a generalized modeling method was established by using the Kane approach. Both the benefits of soft-contact joint and the effectiveness of dynamics equations are verified in MATLAB and Adams software by simulations of a two-joint manipulator with eight-DOF. The comparative simulation results showed the advantages of the proposed soft-contact joint in reducing instability from spatial impact.