At present, diamond wire sawing technology has been widely used in slicing photovoltaic polysilicon. Improving the surface quality of the slices to obtain a sawn surface without microcrack damage can greatly increase the fracture strength of polycsilicon wafers and reduce the cost of wet black silicon texturing, which is beneficial to improve the final photoelectric conversion efficiency of solar cells. In this paper, a mathematical model of diamond wire sawing was established based on the machining mechanism of brittle material removal and surface generation, and the numerical calculation of the sawing process was carried out. The validity of the model was verified by sawing experiments. The critical ratio of workpiece feed speed to saw wire movement speed was obtained when generating a crack-free slice surface under the combination of different process parameters and saw wire parameters. Based on the established theoretical model of sawing, the influence of saw wire movement speed, abrasives density and abrasives size on the critical speed ratio was analyzed, and the critical speed ratio (CSR) corresponding to the finer diameter wire and the higher wire speed which will be gradually applied in industry in the future was analyzed. The research results show that it is more conducive to obtaining a crack-free sawn surface by reducing the workpiece feed speed or increasing the saw wire movement speed, and the workpiece feed speed has a greater impact on the sawn surface quality. The CSR will slightly decrease within a small change range when increasing the saw wire movement speed. Increasing the density of abrasives on the saw wire surface within a certain range or decreasing the abrasives size is more inclined to obtain a crack-free sawn surface. The CSR will decrease slightly in a small range when decreasing the abrasives density or increasing the abrasives average size.