In the elliptical vibration cutting process, the elliptical locus is considered to be a vital factor that affects cutting performance. Besides the cutting speed and vibration amplitudes, the phase shift (i.e., the phase difference between the two-directional output harmonic vibrations forming the elliptical locus) is an intrinsic parameter that determines the shape and inclination of the elliptical locus with respect to the cutting direction. In this paper, a numerical recursive search method is proposed to investigate the effect of phase shift in elliptical vibration cutting. It has been shown that the critical speed ratio for considerably improving the cutting performance has a sinusoidal correlation with the phase shift. For elliptical loci with arbitrary shapes, the developed model theoretically predicts the maximal influential thickness of cut, surface roughness, and the tool-workpiece contact ratio as a function of phase shifts. Experiments were conducted to validate the developed model through the evaluation of the machined surface profile, roughness, and dynamic cutting force. The obtained results offer a method to determine the proper machining variables in cutting hard and brittle materials during the elliptical vibration cutting process with an arbitrary locus.