A substrate cutting apparatus includes a stage configured to support a substrate to be cut along a virtual cutting line, a laser generator configured to emit an ultraviolet (UV)-based laser beam for cutting the substrate by removing part of the substrate along the cutting line, and a beam oscillator disposed on a beam path of the laser beam and configured to perform a beam swing on the laser beam in a direction parallel to the length direction of the cutting line by oscillating a tilt angle of the laser beam toward the cutting line.