Carbon fiber reinforced silicon carbide ceramic matrix composites (Cf/SiC composites) have a wide range of applications in aerospace, nuclear energy, braking systems owing to its excellent mechanical performance. Nevertheless, the hardness, brittleness, heterogeneity, and anisotropy of Cf/SiC composites give rise to difficulties in machining them. In addition, the characterization and formation mechanism of surface damage in the grinding of Cf/SiC composites have not been fully elucidated. The purpose of this paper is to provide a characterization method for surface damage of Cf/SiC composites and an evaluation index for surface edge chipping damage (SECD) through conventional scratching (CS) / ultrasonic vibration assisted scratching (UVAS) tests with single abrasive. Towards revealing the surface damage behavior of Cf/SiC composites during scratching, as well as the impact of fiber orientation on surface damage. The findings indicate that main forms of surface damage of Cf/SiC composites in single abrasive scratching are fiber breakage, fiber fracture-shedding, fiber fracture, fiber-matrix interface debonding, interface fragmentation, matrix cracking, and matrix microcracks. Further, ultrasonic vibration could help to suppress the SECD, and the SECD factor was smallest when scratching along the perpendicular fiber. Furthermore, the fiber orientation can significantly affect the scratching force and cross-sectional area of scratches on Cf/SiC composites via single abrasive scratching. The tangential scratching force was usually smaller as compared to the normal scratching force, and the cross-sectional area of scratches in UVAS is smaller than that in CS. Based on the above findings, this study elucidates the formation and evolution of surface damage after scratching under different fiber orientations, filling the research gap in surface damage under ultrasonic assisted machining of Cf/SiC composites and providing technical guidance for the machining.