In order to ensure the efficient recovery of copper resources, the copper-bearing albite rock samples were taken as the research object, and the impact loads with different strengths were applied by the split Hopkinson pressure bar (SHPB). The crack propagation process was recorded by a high-speed camera system, and the energy dissipation law of the samples under different impact pressures was analyzed by combining the one-dimensional stress wave propagation theory and the law of conservation of energy. At the same time, a numerical model of the impact process of copper-bearing albite is established based on the finite-discrete element coupling algorithm. The results show that the incident energy and the peak stress increase with the increase of the impact gas pressure, and the degree of sample breakage also increases. When the incident energy is less than 140 J, the energy dissipation rate increases with the increase of the incident energy. When the incident energy is greater than 140 J, the energy dissipation rate decreases with the increase of the incident energy, and the energy dissipation rate reaches the maximum when the impact gas pressure is 0.35 MPa. In the process of impact, tensile failure plays a dominant role and forms the main dominant area in the horizontal direction. The new crack area and the total impact energy increase with the increase of impact load. When the impact gas pressure is 0.30 MPa, the strain energy ratio is the smallest. Under this pressure, the proportion of shear cracks is the smallest, indicating that the rock breaking efficiency of 0.30 MPa impact gas pressure is the highest. The numerical model based on finite-discrete element method can effectively predict the damage and fracture process of copper-bearing albite under different impact loads.