Epoxy polymer concrete (EPC) exhibits outstanding properties, including high strength, corrosion resistance, and durability. In recent years, EPC has found extensive application in infrastructure construction projects, often encountering restrictive pressure and cyclic impact loading conditions. By using a split Hopkinson pressure bar device, the dynamic mechanical properties and energy dissipation characteristics of EPC are investigated under varying confining pressures and velocities. A dynamic damage constitutive model for EPC considering strain rate and confining pressure effects is established. The results show that, with a consistent number of impacts, the peak stress of EPC increases with the increasing impact velocity and confining pressure. Moreover, the strain rate rises with the heightened impact velocity but diminishes with the escalating confining pressure. At approximately 360 mu s during the loading process, a transition of the reflected wave from a "tensile wave" to a "compressive wave" occurs, leading to an unloaded rebound phenomenon in the EPC. The evolution of dissipated energy throughout the impact process can be categorized into three distinct stages: a gradual increase stage, a linear growth stage, and a sudden decline stage. The dissipated energy release rate during the third stage ranges from 0.02 to 0.14. Based on the experimental data, constitutive parameters are determined, and a damage constitutive equation considering the effects of confining pressure and strain rate under the cyclic impacts of the EPC is established. The relationships between constitutive parameters and both confining pressure and impact velocity are revealed by surface fitting.