Laser-induced thermal crack propagation (LITP) is a high-quality and efficient processing method that has been widely used in fields such as glass cutting. However, the problem of trajectory deviation often arises in actual cutting operations, especially in asymmetric cutting. To address this issue, a low-temperature gas cooling trajectory deviation correction technique was proposed in this study. This technique modifies the temperature and stress distribution by spraying low-temperature gas onto the processing surface and maintaining a relative position with the laser, thereby correcting the trajectory deviation. The finite element simulation software ABAQUS was employed to numerically simulate the dynamic propagation of temperature fields, thermal stress, and cracks in the asymmetric linear cutting and circular cutting of soda-lime glass with the proposed low-temperature gas cooling trajectory deviation correction technique, and the correction mechanism was elucidated. In the simulation results, the optimal relative distance (ΔX) between the low-temperature gas and scanning laser was obtained by analyzing the transverse tensile stress. Based on the analysis of the experimental and numerical simulation results, it is concluded that the cryogenic gas cooling technique can effectively correct the trajectory deviation phenomenon of asymmetric linear cutting of soda lime glass by LITP.