In this study, a self-modified diamond (SMD) slurry for mechanical polishing is presented as well as a novel TiO2-graphene slurry used with the aid of UV light for a chemical mechanical polishing (CMP) technique that improves the rate of polishing. The surface characteristics and removal rate of silicon carbide (SiC) samples polished with the slurry were compared with the results obtained by polishing with both a conventional diamond slurry and CMP slurry. The experimental results indicated that the material removal rate (MRR) of SiC from the wafer surface with the SMD slurry was higher, and surface finish and lapping efficiency was better than that achievable with other slurries. The experimental data also showed that a TiO2-graphene slurry had a higher removal rate compared to the TiO2 slurry using the same intensity of UV light. The TiO2-graphene slurry showed a 3-fold increase in removal rate over that of a traditional CMP slurry. An experiment was also carried out where nanodiamond (50 nm and 500 nm) abrasive was added to the graphene-TiO2. As expected, the removal rate increased but the average surface roughness was poor because the nanodiamond particles caused small scratches. The graphene-TiO2 with nanodiamond abrasives has 5 times the removal rate achieved with a traditional CMP slurry. This novel method can facilitate the extensive production of well-polished single-crystal SiC wafers.