Hybrid impact drilling is a new drilling method proposed in recent years, the PDC (polycrystalline diamond compact) bit impacts the rock in torsional and axial directions during its rotation. From the perspective of field application, hybrid impact drilling can increase the rate of penetration (ROP), especially in hard heterogeneous formations. However, its rock breaking mechanism and difference from torsional impact drilling are not clear, this leads to aimless in choosing these two drilling methods. In this paper, the quasi-3D numerical simulation model of hybrid impact cutting is carried out to investigate the rock breaking mechanism, including the chip formation, mechanical specific energy (MSE) etc. moreover, its comparison with torsional impact cutting is also conducted for evaluating the applicability of these two methods for the same formation. The results show that, the rock breaking efficiency of hybrid impact cutting is higher than torsional impact cutting for shallow depth of cut (DOC), on the contrary, the rock breaking efficiency of hybrid impact cutting is more lower for the medium DOC; but for the deep DOC, both of these two cutting methods cannot improve the rock breaking efficiency. The axial impact amplitude and frequency have large influence on rock breaking efficiency, the optimal axial impact amplitude and frequency exist for specific formation. Both of these drilling methods are not applicable to soft formations. This study leads to an enhanced understanding of rock breaking mechanisms in hybrid impact drilling, and contributes to the improvement in the design of impact tools and determination of the related parameters.