Machining difficult-to-cut materials has always been a problem to ultra-precision machining due to rapid tool wear. Two-dimensional elliptical vibration cutting (2D EVC) can well alleviate this problem by intermittent cutting motion, but it also has some defects. In this article, a three-dimensional elliptical vibration cutting (3D EVC) apparatus is developed. Four parallel piezoelectric stacks are employed to drive the cutting tool; the tool tip can generate 3D spatial elliptical motions. The spatial positions of generated 3D elliptical motions can be adjusted by varying amplitudes, frequencies, and phase shifts of the actuated signals of piezoelectric stacks; the acting locations of piezoelectric stacks can also be adjusted to satisfy different cutting requirements. Experimental results indicate that the developed 3D EVC apparatus has the feasibility of machining flat surfaces, increasing tool life, and improving machined surface quality compared with conventional cutting and 2D EVC methods.