In this study, a composite cage that integrates many modules, such as a steel frame structure, dive system, energy, and monitoring system, is proposed. It is necessary to conduct hydrodynamic numerical simulation tests to understand the capability to resist waves and currents and ensure the long-term safe and coordinated operation of each system. First, the wave force acting on the cage is calculated based on the potential flow theory. Then, using the motion equation to solve the dynamic response of the cage, a numerical model is constructed to study the potential of the cage under extreme sea conditions. The results indicate that: The dynamic response of the cage in the floating and submerged states is significantly correlated with the wave parameters. The tension of the anchor rope on the upstream side is always greater than that on the downstream side, and the anchor rope tension is positively correlated with the wave height and period in both states. The heave, surge, and pitch are all positively correlated with wave height in both states; it is positively correlated with the period when floating, but has no obvious correlation with the period when sinking. Surge is positively correlated with the period in both states, whereas the pitch is negatively correlated with the period when floating and positively correlated with it period when sinking. The dynamic responses of the cage in the floating and submerged states were significantly correlated with the current velocity. The tension of the anchor rope increases with the increase in flow speed in both states. When the cage is in the floating state, the pitch is positively correlated with the flow speed, the heave is negatively correlated with the flow speed, and there is no obvious correlation between the pitch and the flow speed. The overall variation amplitude of the surge and pitch is between −13% and 20%, and the average variation amplitude does not exceed 7%. When the cage is in the floating state, the maximum heave, surge, and pitch values were 0.549 m, 1.055 m, and 7.116°, respectively. After the cage was submerged, the anchor rope tension, heave, surge, and pitch decreased. The amplitudes were 59%, 70%, 57%, and 49%, respectively, indicating that the cage has a good capability to resist waves and currents. These results have practical significance for improving the safety and efficiency of submersible cage work.