The work aims to accurately predict the subsurface damage of the workpiece, reasonably determine the material removal amount, and optimize the process parameters of the single-crystal sapphire with the fixed abrasive. According to the lapping characteristics of fixed abrasives and the properties of single crystal sapphire, the discrete element model of single crystal sapphire was established by discrete element method, the dynamic process of lapping the material by fixed abrasive was simulated, the generation and propagation of cracks between element particles under load were analyzed, the effect of cut depth of abrasive grains on subsurface damage was studied, the number and depth of subsurface cracks of single crystal sapphire lapped by fixed abrasives were predicted, and the prediction results were verified by chemical corrosion method. The results indicated that with the fixed abrasive pads with particle sizes of W14, W28, W50 and W65, the corresponding predicted depth of the lapped sapphire subsurface damage layers was 3.75 μm, 5.28 μm, 7.62 μm and 10.92 μm; the predicted number of cracks was 199, 236, 526 and 981; and the corresponding experimental values were 3.79 μm, 5.88 μm, 8.76 μm, and 11.44 μm, respectively. As the abrasive particle size in the fixed abrasive pad increased, the depth of the single crystal sapphire subsurface damage layer and the number of cracks also increased. The comparison showed that the measured values and predicted values were basically consistent, and the correctness of the prediction results was verified. Therefore, the discrete element method can quickly and effectively predict the number and depth of cracks in the sapphire subsurface damage layer of the fixed abrasive, and provide guidance for the optimization of the lapping process parameters and the formulation of subsequent polishing process parameters.