The super-precise theory for machining single crystal SiC substrates with abrasives needs to be improved for its chemical stability, extremely hard and brittle. A Berkovich indenter was used to carry out a systematic static stiffness indentation experiments on single crystal 6H-SiC substrates, and then these substrates were machined by utilizing fixed, free, and semi-fixed abrasives, and the nanomechanical characteristics and material removal mechanisms using abrasives in different fixed methods were analyzed theoretically. The results indicated that the hardness of C faces and Si faces of single crystal 6H-SiC under 500 mN load were 38.596 Gpa and 36.246 Gpa respectively, and their elastic moduli were 563.019 Gpa and 524.839 Gpa, respectively. Moreover, the theoretical critical loads for the plastic transition and brittle fracture of C face of single crystal 6H-SiC were 1.941 mN and 366.8 mN, while those of Si face were 1.77 mN and 488.67 mN, respectively. The 6H-SiC materials were removed by pure brittle rolling under three-body friction with free abrasives, and the process parameters determined the material removal modes of 6H-SiC substrates by grinding with fixed abrasives, nevertheless, the materials were removed under full elastic-plastic deformation in cluster magnetorheological finishing with semi-fixed abrasives.