The work aims to study effects of relevant technological parameters on cutting parameters by simulating abrasive jet flow erosion and cutting with LS-DYNA. Based on the single abrasive water jet single-point erosion simulation and cutting simulation, both water and abrasive particles were modeled in the method of SPH, alumina ceramic workpiece was modeled in the method of FEM, and jet erosion and cutting process was simulated through SPH-FEM coupling algorithm. According to simulation analysis of jet erosion process and cutting process, abrasive collision and rebound contributed to irregular "V" type wall in early stage of jet machining. At the initial phase, cutting depth increased linearly as time prolonged; the wall had a restrictive effect on the abrasives, therefore hole depth in machining position no longer increased. The abrasives erosion at the bottom of the wall enabled the pit bottom width to increase and tend to be stable rapidly. Meanwhile, there is certain difference between cutting simulation and erosion simulation as the cutting process has set movement speed. Comparison of simulation results with experimental results shows that cutting depth increases linearly as pump pressure increases, increases as the abrasive flow rate increases, and decreases as target distance and traverse speed increases. The cutting depth has nonlinear relationship with abrasive flow rate, target distance and traverse speed; maximum workpiece cutting depth does not grow linearly as and calculation time prolongs.