To predict fragment separation during rock cutting, previous studies on rock cutting interactions using simulation approaches, experimental tests, and theoretical methods were considered in detail. This study used the numerical code LS-DYNA (3D) to numerically simulate fragment separation. In the simulations, a damage material model and erosion criteria were used for the base rock, and the conical pick was designated a rigid material. The conical pick moved at varying linear speeds to cut the fixed base rock. For a given linear speed of the conical pick, numerical studies were performed for various cutting depths and mechanical properties of rock. The numerical simulation results demonstrated that the cutting forces and sizes of the separated fragments increased significantly with increasing cutting depth, compressive strength, and elastic modulus of the base rock. A strong linear relationship was observed between the mean peak cutting forces obtained from the numerical, theoretical, and experimental studies with correlation coefficients of 0.698, 0.8111, 0.868, and 0.768. The simulation results also showed an exponential relationship between the specific energy and cutting depth and a linear relationship between the specific energy and compressive strength. Overall, LS-DYNA (3D) is effective and reliable for predicting the cutting performance of a conical pick.