Button cutters are commonly used in hard rock drilling because the inserted carbide buttons provide exceptional wear resistance, impact resistance, and high strength in challenging geological formations. One of the most pressing issues in designing a button cutter is to study the rock breaking mechanisms of carbide buttons. In this study, the three-dimensional discrete element method (DEM) was employed to investigate the rock breaking mechanism and cutting performance of five widely used carbide buttons, i.e., spherical, saddle, wedge, conical, and parabolic buttons. The simulation results were compared with laboratory tests to reveal the rock indentation process. The crack propagation pattern, energy dissipation, and damage evolution associated with the force–penetration depth curve were investigated. Tensile damage was the primary determinant for crack propagation and coalescence. By systematically exploring the penetration index, specific energy, and crack propagation characteristics, the conical button had a high rock breaking efficiency when the penetration depth was low, and the saddle button had a high rock breaking efficiency when the penetration depth was high. The findings can provide references for the design of a button cutter.