Laser internal modification processing technology, with its high efficiency, non-contact, and low loss advantages, is widely used in the field of semiconductor wafer cutting. To investigate the influence of laser focusing characteristics at different depths within the wafer on cutting quality, a spherical aberration correction was performed using the backward ray-tracing method. An experimental platform for laser internal modification cutting, based on spherical aberration correction via a liquid crystal spatial light modulator, was designed and constructed. Using a 1064 nm picosecond laser, experiments were conducted on a 350 μm thick silicon carbide wafer, resulting in an internal laser modification layer with a length reduction of 20%~30%. Furthermore, based on the energy loss of laser transmission within the material and the change in laser power density caused by spherical aberration correction, a method for regulating the focusing characteristics of laser internal modification cutting for silicon carbide wafers was proposed. The results indicated that by employing a variable power multi-pass scanning strategy, high-quality processing with a side surface roughness 819 nm and no edge or corner chipping was achieved using eight modification layers. This study provides a reference for optimizing the laser internal modification cutting process and enhancing the cutting quality of silicon carbide wafers.