The existing mechanical dicing process of single crystalline Silicon Carbide (SiC) is one of the main factors limiting the development of semiconductor process, which could be replaced by laser dicing potentially. However, the zones of ablation damage generated by high power laser should be well controlled. When wafer is only scribed with a thin groove by laser, thermal effect could be reduced significantly. The while scribing process includes laser grooving and subsequent mechanical cracking. The mechanical cracking by force is critical to determine the finishing quality, and spallation or irregular cross-section may be obtained if the cracking process is uncontrolled. The initiation and propagation of the crack are related to the geometry of scribed groove and the melted layer in the groove. To achieve efficient and low-damage SiC separation, the cracking behavior of SiC after laser grooving should be addressed and controllable. Since the laser grooving including thermal ablation and meltage solidification, the cracking behavior of the scribed SiC would be different to the original single crystal SiC. In this paper, cohesive zone model (CZM) is used to quantitively represent the cracking behavior of the scribed SiC. Nanosecond laser with different processing parameters is adopted to scribe SiC substrate with different geometries of grooves. To capture the cohesive behavior of the scribed SiC during cracking, the whole separation of the SiC was conducted in a three-point bending (3PB) fixture. Therefore, by inverting the load-displacement curves of 3PB with CZM embedded finite element model (FEM), the cohesive behavior is characterized by bilinear traction-separation law, which illustrated the whole cracking process numerically. The methodology established in current paper gives way to understand the SiC scribing and cracking process with quantitative cohesive parameters.