Cracking behavior caused by the anisotropy of single-crystal silicon carbide (SiC) brings challenges to the quality of the diamond wire sawing and grinding process. In this study, the effects of SiC anisotropy on machanical properties is analyzed based on Griffith’s theory. The results indicate that the fracture toughness and the fracture strength exhibit anisotropy. At the same time, an analytical model for the initiation and deflection of the surface radial crack is proposed based on the scratching stress field. On the basis of these results, the anisotropic machanism of the surface radial crack initiation, deflection, the surface radial crack initiation (SRCI) depth, and the residual scratching depth are investigated in combination with the single abrasive scratching experiment. The shear stress and the maximum principal stress are the primary driving forces for the initiation and deflection of surface radial crack, respectively. The direction of the minimum shear strength and the fracture strength determines the anisotropy of cracking behavior. Meanwhile, the anisotropy of the SRCI depth and the residual scratching depth is caused by the fracture strength anisotropy. This research offers fundamental insights into the anisotropic cracking behavior of SiC, thereby contributing to the precise control of crack damage and improve the quality of the SiC diamond wire sawing and the as-cut wafers grinding process.