To investigate the overtopping and slamming phenomena that occur in the interactions between waves and oscillating surge wave energy converters (OSWECs), a two-dimensional numerical wave flume was established using computational fluid dynamics (CFD) software Fluent by adding the momentum source terms into the original Navier–Stokes equation. Numerical convergence studies of the mesh sizes and time steps were firstly performed to ensure the sufficient accuracy of the numerical model. The variations in the wave heights along the wave propagation direction in the wave-generating area, working area, and wave-absorbing area were analyzed. The dynamics of the flap-type OSWEC were simulated using the overset mesh function embedded in Fluent. In addition, the numerical results were compared with the experimental data, and good agreements were achieved. External torque was applied to the hinge joint of the OSWEC to simulate the forces due to the power take-off (PTO) system, and the identified optimal PTO damping was compared with the numerical results based on the potential flow theory, which verified the correctness of the numerical PTO system. On this basis, nonlinear wave slamming by the sharp-eagle OSWEC was analyzed. The results show that under certain incident wave conditions, the sharp-eagle OSWEC can effectively reduce the maximum rotation angle and angular velocity compared with those of the flap-type OSWEC, and there is no overtopping that occurring for the sharp-eagle OSWEC. Furthermore, the sharp-eagle OSWEC performs better than the flap-type OSWEC.