During actual service of the reservoir dam, there always appears a combination of water level fluctuations, rainfalls, and other hazard factors. During these times, the safety state of the dam is a dynamic process, and the dynamic risk assessment of dam slope stability which considers the time scale is of great importance. Therefore, in this study, the dynamical stability of the earth-rock dam under the combined action of multiple hazards is studied by using the Monte Carlo method, considering the spatial variability of the soil of dam and the coupling effect of the seepage field and the stress field. The failure probability and reliability index of dam under each working condition are calculated to determine the most dangerous working condition during the disaster-causing process. For the upstream slope, the most dangerous condition appears at the moment when the water level drops at a rate of 2 m/d with a 40 mm/d rainfall intensity, while the most dangerous condition of the downstream slope is that when the water level rises at a rate of 2 m/d with a 40 mm/d rainfall intensity. The influence of various disaster factors on the stability of dam is revealed and corresponding engineering early warning measures are proposed. This study realizes the dynamic risk assessment of dam slope stability under multiple hazards, avoids the limitation of evaluating the dam slope stability with a single safety factor, and provides a reference for risk analysis and emergency management of reservoir dams under the action of multiple hazards.