This paper gives a brief explanation of the failure mechanism of rock fragmentation in rock cutting. The JOHNSON_HOLMGIST_CONCRETE is selected as the rock material model in numerical simulation with confining pressure and damage influence introduced. We use the non-linear dynamic finite element software LS/DYNA to simulate the dynamic process of cutting rock. The cutting forces acting on disc cutter are computed. The relationship between cutting forces and penetration depth, confining pressure and damage parameters are obtained. The results show that, the cutting forces increase with the penetration depth. They are larger in equal confining pressure than unequal condition. The forces are amplified with the damage parameters increasing. The conclusion provides a reference for the prediction of the cutting forces.