The sprag clutch-accessory gear transmission system is a critical component for mode switching in the new hypersonic engine. During mode switching, the engine generates internal impacts within this system, resulting in significant impact loads that severely compromise the operational safety of the engine. These impact loads primarily occur during the wedging process of the sprag clutch between the two power sources. Currently, there is a lack of effective evaluation methods to assess the impact resistance of the transmission system under different engagement conditions, and the influence of various parameters on the dynamic response of the sprag clutch remains poorly understood. To address these issues, this paper establishes a dynamic model for mode conversion in the accessory transmission system of the new hypersonic engine using the explicit dynamics software LS-DYNA. The study investigates the dynamic stress and wedging performance under typical engagement conditions. The results reveal that the clutch undergoes three distinct stages during the engagement process: the slippage stage, the unstable engagement stage, and the stable combination stage. During the unstable stage, a significant sprag contact force is generated, which adversely affects the transmission system. This leads to increased gear impact and higher contact forces on the spline, thereby elevating the risk of system failure. This study provides theoretical insights and guidance for the parameter selection and operational condition determination of the sprag clutch, contributing to the improved design and safety of the transmission system.