Based on the theoretical analysis of kinematics principles of the abrasive, dimensionless parameter K was defined to describe the impact effects. Smooth Particle Hydrodynamics (SPH) Finite Element Method was used to study the mechanisms of crack formation and extension in the interior of the material under the impact of the abrasive. The simulation results showed that, with the increasing of K, the inclination and the depth of the inclined crack decreased. The interaction mechanisms between the abrasive and the workpiece showed that the impact of the abrasive was the main reason for the crack formation and extension. In the cutting process, the cutting force increased rapidly, and then, due to the formation of the cracks, the vertical impact forces reduced dramatically, but the horizontal impact force changed little. As the local micro-impact phenomenon between the material and the abrasive, the cutting forces in both directions fluctuated within a relatively large range.