Abrasive suspension jet (ASJ), an accurate cold-cutting technology, can address traditional processing issues relating to carbon-fiber-reinforced plastics (CFRPs) like tool wear, interlayer delamination, large heat-affected zone, and low surface roughness. This study employed the use of an ASJ to cut CFRPs and an ultra-depth optical microscope to scan the cut surface to analyze interlayer delamination, surface roughness, kerf taper, and shoulder damage. Regression analysis was conducted to establish a prediction model for cutting quality based on surface roughness, kerf taper, and shoulder damage. Various types of CFRP cutting quality were analyzed using jet parameters. It was found that the use of ASJ to process CFRP results in the following defects: The range of surface roughness variation is from 0.112 μm to 0.144 μm. Surface roughness is most influenced by stand-off distance, followed by traverse speed and jet pressure. The range of kerf taper variation is from 4.737° to 10.1°. Kerf taper is most influenced by stand-off distance, followed by jet pressure and traverse speed. The range of shoulder damage variation is from 3.384 μm2 to 10 μm2. Shoulder damage is most influenced by jet pressure, followed by traverse speed and stand-off distance. A prediction model for cutting quality was developed based on surface roughness, kerf taper, and shoulder damage, providing data support for ASJ cutting of CFRPs. The optimal parameter combination is a stand-off distance of 1 mm, a jet pressure of 30 MPa, and a traverse speed of 30 mm/min.