Silicon carbide (SiC) single crystal has many advantages comparing with silicon single crystal, such as wide band-gap, hardness and various stable physical properties at high temperature and severe chemical environments. SiC semiconductor substrate is expected to be applied to high power devices and sensor devices in the severe environments. The polishing process under ultraviolet-ray irradiation has been developed in our laboratory to achieve the mirror-finish process of single-crystal SiC. In this paper, after the confirmation of the elastic deformation behavior of SiC single crystal using the nano-indentation tester, pre-processings of SiC by lapping and constant-pressure grinding were performed to obtain good surface without brittle fracture region. The indentation tests indicate the single-crystal SiC shows a very high elastic recovery rate. SiC substrate was processed by the lapping and the constant-pressure grinding using the constant-pressure processing to avoid the cumulative residual stock removal. As many experimental results, the constant-pressure grinding is found to be suitable for the pre-processing of SiC substrates. Additionally, it is clarified that good surface roughness on the ground surface is achieved by using a diamond wheel with the same protrusion height of abrasive grains.