For precise micro-grooving and surface machining, a mechanism for creating elliptical vibration cutting (EVC) motion is proposed which uses two parallel piezoelectric actuators. And based on its kinematical analysis, variations of EVC path are investigated as a function of dimensional changes in the mechanism, phase difference and amplitude of excitation sinusoidal voltages. Using the proposed PZT mechanism, various types of two dimensional EVC paths including one dimensional vibration cutting path along the cutting direction and thrust direction can be easily obtained by changing the phase lag, the amplitude of the piezoelectric actuators, and the dimension of the mechanism.