Laser thermal effects can cut glass by inducing stress, but high temperatures may lead to burns or thermal cracks. This paper employs ABAQUS to study temperature distribution and heat time-integral flux (HTL) influence during laser induced thermal-crack propagation (LITP), examining how HTL impacts ablation, surface morphology, roughness, and straightness to establish a threshold for undamaged cuts. The results indicate that: when the HTL is lower than 14.5 J/cm³, the laser energy is not sufficient to cut the glass effectively; in the interval of 14.5307.2 J/cm³, the cut cross-section and the surface of the glass samples are smooth, straight, and damage-free; when the HTL is higher than 307.2 J/cm³, the cut cross-section starts to show obvious thermal damage, ablation, and chipping of the cut edges.