A glass substrate slicing apparatus is disclosed, which comprises a laser emitting device and a slicing device. The laser emitting device is adapted to emit a laser beam onto a surface of a glass substrate to be sliced so as to form micro-grooves on the surface of the glass substrate; and the slicing device is adapted to slice the glass substrate at locations of the micro-grooves, and comprises a wheel cutter fixing device and a diamond wheel cutter fixed on the wheel cutter fixing device. A laser beam is emitted by the laser emitting device to form micro-grooves on a surface of the glass substrate so that a diamond wheel cutter can be inserted into the micro-grooves to slice the glass substrate at locations of the micro-grooves. As a result, the frictional force between the diamond wheel cutter and the glass substrate can be enhanced to prevent slipping of the diamond wheel cutter during the slicing process, thus improving the slicing accuracy.