Torsional percussive drilling tool was designed to reduce the risk of stick-slip and improve drilling efficiency, but there are few studies on the influence of torsional impact parameters, including amplitude, frequency, waveform, on the rate of penetration (ROP) while drilling the hard rock. The design of the torsional percussive drilling tool was proposed, and the mathematical model of torsion hammer movement was developed, the Riedel-Hiermaier-Thoma (RHT) rock dynamic material model was applied to analyze the rock-breaking process of the tool. A numerical model of hard rock cutting with a single polycrystalline diamond composite (PDC) bit cutter was established, the influences of amplitude, frequency, time parameters, and waveforms on the penetration depth of the PDC bit cutter were analyzed in the process of torsional percussive drilling. The results showed that the numerical simulation results were in good agreement with the indoor test results, which verified the correctness of the numerical simulation. Compared with conventional drilling, the penetration depth of torsional percussive drilling was increased by 20.0%, and the cutting debris particles were smaller, which was conducive to improving ROP and reducing stick-slip vibration of the bit. With the increase of the peak value of torsional percussive amplitude, the penetration depth of the cutter first increased and then decreased. When the ratio of torsional impact load to axial static load was 1.0, the penetration depth of the drilling cutter reached a maximum. When the torsional impact frequency was 40 Hz–100 Hz, the penetration depth decreased with the increase of the frequency, but the diameter of cuttings became smaller and smaller, which was conducive to cleaning the wellbore with drilling fluid. The latter has the highest rock-breaking efficiency compared with triangular, sine, and rectangular waves. Finally, suggestions are given on how to adjust these parameters by adjusting engineering parameters and tool structure parameters to optimize the efficiency of the torsional percussive drilling tool.