To more accurately simulate the interaction between a polycrystalline diamond compact (PDC) cutter and rock, the structural characteristics of basalt were analysed using computed tomography (CT), and a hard particle–matrix–pore three-phase rock model was established due to its structural characteristics. Three-dimensional models of the interaction between PDC cutters and rock were established by using the finite–discrete element method (FDEM). Using Voronoi diagrams to randomize the grid structure and optimize the propagation of cracks. This study revealed that a broken zone near the cutters will form during the rock breaking process, resulting in the affected area being larger than the area in contact with the formation rock. The rock breaking ability of circular cutters is stronger than that of conical cutters. When a conical cutter breaks hard particles, they are mainly striped or forced away from the rock, but circular cutters can divide hard particles into small pieces. The numerical model used in the research institute can effectively calculation results of the process of interaction between PDC cutter and rock, this proves that the application of the cohesive method to simulate rock breaking by PDC cutters is reliable.