This study investigates the dynamic response and power generation performance of a self-accelerating gyroscopic wave energy converter (GyroWEC) under roll and pitch motions in autonomous vessels. This article introduces the structural design and power generation principle of the GyroWEC. Considering the roll and pitch motions, a comprehensive dynamic model of the wave-ship-GyroWEC system is established. Then, a prototype is developed, and experiments are conducted. Combined with numerical computations, the dynamic response characteristics of the GyroWEC under roll and pitch motions are validated. The influence of roll amplitude, speed ratio, precession equilibrium angle, and encounter angle on the performance of the GyroWEC is investigated. The results indicate the following: Under constant pitch excitation, increasing roll amplitude correlates with a decrease in the power generation capacity of the GyroWEC. The power capture of the GyroWEC initially increases and then decreases with the speed ratio. Under the conditions of flywheel diameter of 640 mm, flywheel weight of 78 kg, pitch excitation (period: 4 s, amplitude: 15°), and a speed ratio of 25, the device achieves its peak power capture of 38.8 W. Adjusting the precession equilibrium angle can enhance the power generation capability under roll and pitch motions. Even at large encounter angle, the adjustment of precession angle remains effective for promoting the power absorption.