One-step raise excavation with burn cut is a kind of technology which use the drilling and blasting method to excavate the raise quickly. Due to the limitation of the free surface in burn cut, determination of cut parameters such as the length of burden and diameters of empty hole and charge hole is important to achieve a good effect of cut blasting. Meanwhile, the choice of the cut model is also crucial to form a proper opening. In this study, a modified Holmquist-Johnson-Cook (HJC) model, in which the tension-compression damage model and tension-compression strain rate effect model are considered, is embedded in the LS-DYNA software to investigate the damage evolution of rock in cut blasting. A simplified numerical model of burn cut is built in the LS-DYNA. The numerical results indicate that there is a threshold value of the burden length to maximize the opening. The empty hole has the effect of transferring blasting energy, and the effect becomes more obvious with the increase of the hole size. Moreover, the linear charge density of the prime cut hole can affect the compression and tension damage. Further, the comparison among four typical burn cut models are conducted based on numerical results. It demonstrates that triangular prism cut and doliform cut, which have more empty holes arrangement surrounding the prime cut hole, are better than spiral cut and diamond cut that with less empty holes locating one side of the prime cut hole in terms of energy efficiency and damage zone control.