The longitudinal–torsional ultrasonic vibration machining process is popular for machining hard and brittle materials. A longitudinal–torsional ultrasonic vibration system with diagonal slits was designed for the ultrasonic vibration machining process based on the principle of acoustics propagation in this study. Four uniform diagonal slits were cut off on the horn cylinder to transform the longitudinal ultrasonic vibration into a longitudinal–torsional composite motion. A finite element analysis was used to optimize the mechanical structure of the vibration system. Dynamic characteristics of the vibration system were numerically studied, and the relationship of diagonal slits versus the resonance frequency and amplitudes of longitudinal–torsional vibration was analyzed, so that the longitudinal–torsional output amplitude can be optimized by rational choice of structure parameters of diagonal slits. Moreover, the movement locus of the system output end was obtained by utilizing the Origin software, which was proved to be elliptical, and the accuracy of the finite element model was confirmed by comparing numerically and experimentally determined resonant characteristics. In addition, the verification of longitudinal–torsional ultrasonic vibration was proved for the designed ultrasonic vibration system.