Nanoscale surface roughness of tungsten heavy alloy components is required in the nuclear industry and precision instruments. In this study, a high-performance ultrasonic elliptical vibration cutting (UEVC) system is developed to solve the precision machining problem of tungsten heavy alloy. A new design method of stepped bending vibration horn based on Timoshenko’s theory is first proposed, and its design process is greatly simplified. The arrangement and working principle of piezoelectric transducers on the ultrasonic vibrator using the fifth resonant mode of bending are analyzed to realize the dual-bending vibration modes. A cutting tool is installed at the end of the ultrasonic vibration unit to output the ultrasonic elliptical vibration locus, which is verified by finite element method. The vibration unit can display different three-degree-of-freedom (3-DOF) UEVC characteristics by adjusting the corresponding position of the unit and workpiece. A dual-channel ultrasonic power supply is developed to excite the ultrasonic vibration unit, which makes the UEVC system present the resonant frequency of 41 kHz and the maximum amplitude of 14.2 μm. Different microtopography and surface roughness are obtained by the cutting experiments of tungsten heavy alloy hemispherical workpiece with the UEVC system, which validates the proposed design’s technical capability and provides optimization basis for further improving the machining quality of the curved surface components of tungsten heavy alloy.