A simulation approach was utilized to investigate the mechanics of cutting rock using the diamond circular saw blade in this paper. The smoothed particle Galerkin (SPG) method was used to numerically simulate three factors, including the dynamic mechanical behavior of the circular saw blade, the damage law of the circular saw blade, and the cutting force of the saw blade. The experimental comparison indicated that the SPG approach is feasible and accurate in the analysis and simulation of the rock cutting mechanism. The rock cutting is a process of material cyclic removal. The wear parts of the saw blade are most obviously manifested at the end of the saw segments. The water groove is also readily damaged in the alternating action, which has a significant impact on the service life of the saw blade. The effects of speed, cutting depth, and feed speed on the cutting force are discussed. The results reveal that these mentioned factors are important to the quality of rock cutting.