Abstract: The axial-torsional composite impact assisted drilling technology can effectively improve the rock fragmentation efficiency of PDC bits in deep and ultra-deep formations. However, current research on the relationship between the axial-torsional impact velocity amplitude and the frequency ratio for PDC cutters (including their worn state) under combined impact is still insufficient, leading to a lack of theoretical basis for optimizing impact parameters and limited improvement in rock-breaking efficiency. Therefore, it is necessary to conduct a systematic study on this relationship. Based on the discrete element method, a heterogeneous granite model was constructed, and numerical simulations were conducted on its dynamic fragmentation behavior under the combined action of PDC cutter impact cutting with different ratios of axial-to-torsional impact velocity amplitude and axial-to-torsional impact frequency. The rock fragmentation characteristics were analyzed from multiple aspects. The results indicate that rock fragmentation effectiveness is better under impact cutting with a larger axial-to-torsional impact velocity amplitude ratio and a smaller axial-to-torsional impact frequency ratio, and it is recommended to adopt ratios of 4:1, 2:1 or 3:1, 1:1. Furthermore, under these conditions, worn PDC cutters with a certain degree of wear can promote rock fragmentation to some extent, although this effect disappears when the wear becomes excessive. When the axial impact velocity amplitude is large, the axial impact frequency can be appropriately increased to obtain a larger cuttings volume, while the opposite approach should be taken when the axial impact velocity amplitude is small. Under the combined action of impact and cutting, rock failure is predominantly tensile in nature, with over 70% of tensile cracks tending to propagate in the vertical direction, among which cracks with dip angles exceeding 80° account for 20%. The research findings have certain value for improving rock fragmentation efficiency in deep and ultra-deep formations.