Carbon fiber reinforced carbon and silicon carbide matrix composites (C/C-SiC) have a great potential in industrial applications due to their high friction coefficient and wear resistance, however, few published researches have studied systematically on the drilling of C/C-SiC composites, and the machinability can be problematic when drilling due to their anisotropy. Therefore, to reduce the surface damages of the drilled hole on unidirectional C/C-SiC composites, the drilling experiments with supported graphite plate are carried out systematically with brazed diamond drills, and the results are compared with that without supported graphite plate. The effect of process parameters on thrust force, delamination factor, hole surface quality and tool wear is investigated. Results show that the drilling with supported graphite plate improves the surface integrity of drilled hole compared with that without supported graphite plate. The thrust force increases with the reduced cutting speed and increasing feed rate. High spindle speed and low feed rate are effective in reducing the delamination factor and improving the drilled hole quality. Meanwhile, it is found that the surface damages and damage mechanisms of the drilled hole are influenced by the fiber orientation and cutting direction. Finally, the wear mechanisms of the drills with different process parameters are analyzed.