In recent years, with the rapid development of soft robots, dielectric elastomer actuators (DEAs) as a novel type of soft actuators have been widely studied. However, DEAs often suffer from low instantaneous output force/power, especially in high payload damping conditions, which limits their applications in certain scenarios. Inspired by the vibro-impact mechanisms found in many engineering systems (e.g., pile driving and percussive drilling), a resonant-impact DEA system was proposed in the authors’ previous work to potentially address this limitation. However, due to the complex nonlinearities and unique electromechanically coupled forcing mechanism of DEAs, no nonlinear dynamic model was developed to perform systematic investigations and optimization. In this paper, a nonlinear dynamic model of the resonant-impact DEA system is developed by considering multiple nonlinearities, viscoelasticity, and electromechanical coupling. Using both a numerical model and extensive experiments, the nonlinear dynamics of the resonant-impact DEA system are studied in depth. The effects of several key parameters, including excitation voltage amplitude, constraint gap, constraint stiffness, and number of DEA layers, on the dynamic response of the system are characterized. The findings reported in this paper can provide guidance for the performance optimization of resonance-impact DEA systems and their applications.