Abrasive particles play a vital role in the impact on materials during abrasive waterjet cutting. To study the effect of particles on the cutting performance during abrasive waterjet cutting, the mostly irregular shape of the abrasive particles in the actual cutting process needs to be considered. In this paper, the particles are simplified as angular and circular particles. The method of Smoothed Particle Hydrodynamics (SPH) is used to simulate the process of particle impact targeting in abrasive jet cutting. Because the abrasive particle impact causes a large local deformation or removal of the surface of the target material, the traditional grid-based numerical method is not suitable for such problems; thus, the SPH method, which is suitable for the impact problem, is selected to establish the numerical model and solve it. In this paper, the fracture process of abrasive particles with different shapes of impact ductility and brittle target materials is studied by a numerical model. In the modeling process, abrasive particles are modeled as rigid bodies with material properties, the ductile materials is an aluminum alloy, the brittle material is quartz glass, which are simulated by changing the initial input conditions and particle shape, and the model is verified by experiments. The results show that the model successfully reproduces the collision process of particles during abrasive jet cutting, including the deformation mechanisms of plowing, fracture and crushing of the target.