Introducing ultrasonic vibration into the shearing process of hard-to-deform magnesium alloy sheets shows the potential to solve the problems of poor-quality sheet sections and excessive burrs. In this paper, for the AZ31B magnesium alloy sheet, the method of constructing a converter to connect the displacement and vibration reference points is used to establish an ABAQUS three-dimensional ultrasonic vibration shearing simulation analysis model. Furthermore, the processing characteristics of ultrasonic shearing are described by analyzing the equivalent stress. Subsequently, the influence weight coefficients of three factors, sheet temperature, shear edge clearance, and ultrasonic amplitude, and the influence law of the above factors on the change of stress in ultrasonic shearing processing, are studied using the orthogonal test method. The results show that, since ultrasonic vibration can produce intermittent contact and ultrasonic energy softening effect on magnesium alloy sheets, shear processing equivalent stress appears as the phenomenon of stress superposition and fluctuation. Therefore, the equivalent stress of ultrasonic shearing under the same process parameters is less than that of conventional shearing. Moreover, ultrasonic shearing processing of magnesium alloy sheets through the plastic deformation phase for an extended time improves the quality of the shear section. The process parameter with the most significant influence factor in ultrasonic shearing is the sheet temperature, followed by the shear edge clearance and the smallest ultrasonic amplitude. This paper can provide quantitative guidance for the predictive assessment of the ultrasonic shearing quality of the AZ31B magnesium alloy sheet.