A wave-assisted propulsion (WAP) system involves a hydrofoil attached to a surface vehicle via linear and/or torsional spring systems. The hydrofoil undergoes a flapping motion that is induced by the surface waves and in doing so, generates thrust. A well designed WAP system could enable effective propulsion that uses no or very little external power. The performance of a WAP system however depends strongly several parameters and the flow-physics and fluid-structure interaction that determines the performance is not well understood. This creates a challenge for understanding and optimizing the performance of these systems. In the present study, the hydrodynamics and associated thrust performance of WAP systems are investigated by high-fidelity computational flow models and new data-enabled analysis tools. The effects of kinematic parameters on the performance and stability of the WAP system are systematically investigated by generating the thrust and energy maps and the stable, wave-driven operating conditions are verified by the fluid structure interaction simulations. The thrust generation mechanism is then dissected by applying the force partitioning method. From the simulations and analysis results, a new scaling parameter for predicting thrust performance is derived and verified