The problem of controlling coupled six-degrees-of-freedom (6-DOF) relative motion of an integrated-actuation spacecraft in the presence of actuator faults, and especially failures, is investigated in this paper. Considering the complications and limitations of the common control paradigm (which requires a mathematical model of a plant), a novel data-driven control framework is proposed. Specifically, the subspace predictive control (SPC) approach (which is an elegant data-driven framework based on a special combination of the model predictive control method and the subspace system identification technique) is developed and extended to control nonlinear plants and to tolerate abrupt and severe faults. Accordingly, a model-free fault-tolerant control method for coupled nonlinear time-variant plants is provided, such that its only fault diagnostic requirement is detection of the occurrence time of faults. Furthermore, a fully decentralized multispacecraft strategy is proposed and formulated that is quite suitable for a data-driven cooperative control approach. The effectiveness of the developed framework is demonstrated via simulation.