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In view of the stick-slip phenomenon in deep and hard rock drilling, a new type of torsional impactor that can provide torsional impact vibration was designed. According to the working principle and structural characteristics of the designed torsional impactor, this paper theoretically analyzes the influences of different structural parameters and motion parameters on the impact frequency, impact force, and impact torque of the torsional impactor. The results show that the impact frequency <i>f</i> is directly proportional to the rotational speed <i>V_Z</i> of the transmission shaft and the installed number <i>n</i> of torsional impact generating devices. Additionally, the impact force <i>F</i> is directly proportional to sine value of the impact angle <i>α</i> (i.e., sin<i>α</i>), impact hammer mass <i>m</i>, impact hammer rotation speed <i>V_Z</i> (i.e., transmission shaft rotation speed), and impact hammer rotation radius <i>r</i> and is inversely proportional to action time Δ<i>t</i> of the impact hammer and impact anvil. Furthermore, the impact torque <i>M</i> is directly proportional to the impact force <i>F</i> and rotary radius <i>r</i> of the impact hammer. This article lays a foundation for further theoretical and experimental research of torsional impactors and provides a reference for the design and testing of torsional impactors.