Abstract: Composite impact drilling is a novel rock-breaking technique that combines both axial and torsional impacts. To address the issues of complex failure mechanisms and unclear rock-breaking mechanisms under the axial-torsional impacts on rock by Polycrystalline Diamond Compact (PDC) drill bits, a FEM-DEM rock model based on shared nodes was established using the Continuous Discontinuous Element Method (CDEM), and the rationality of this computational model was verified through laboratory uniaxial compression experiments. Besides, a composite impact motion model for single drill bit was built through the secondary development of JavaScript, and the composite impact rock-breaking process of single PDC drill bit under a sine function was simulated. In addition, the failure patterns of rock under composite impact were revealed by analyzing the formation processes of rock fragments, radial shear cracks, lateral cracks, and lateral main cracks. Based on this, a mechanical model for the penetrating force of a single drill bit under the composite impact was established, and a continuous-discontinuous numerical algorithm suitable for the analysis of rock-breaking drilling under composite impact was developed. Meanwhile, the rock-breaking effects under different penetration depths, rake angles, axial impact velocities and torsional impact velocities were analyzed, and the penetrating force values and rock-breaking patterns under different drill bit parameters were discussed. The results show that: composite impact is a process that fully integrates the advantages of axial and torsional impacts, which optimizes the energy distribution of the entire drilling system. Under the composite impact, the rock in front of and below the drill bit is extensively fragmented, achieving a “three-dimensional rock-breaking” effect and reducing the stick-slip effect of the drill bit. Definitely, the contact area, the contact arc length and the distribution of impact energy between the drill bit and the rock formation are the key factors affecting the efficiency of rock breaking by composite impact. Specifically, the rock breaking volume increases with the increasing drilling depth, but the penetrating force applied to the drill bit also increases simultaneously. The impact angle will affect the horizontal and vertical distribution of impact energy, and a greater volume of rock would be broken by the drill bit at a small rake angle. Increasing the axial and torsional impact velocities could increase the rock breaking volume, but a larger penetrating force may be applied to the drill bit, which is unfavorable to extend the service life of the drill bit. Generally, the research results are of referential significance for improving the rock-breaking efficiency under different working conditions, optimizing the design parameters of PDC drill bit, and extending the service life of the drill bit.