Carbon fiber reinforced plastic (CFRP) composites provide excellent properties, which make them attractive in many industries. However, due to the properties of high stiffness, anisotropy, and high abrasiveness of carbon fiber in CFRPs, they are regarded as difficult-to-cut materials. To find an efficient surface grinding process for CFRP, this paper conducts an investigation using RUM. Design of experiment (DOE) is vital to evaluate effects of input variables on output variables, and it could be used to obtain the optimal values of variables in such a process. DOE could also be used to decrease the test numbers, the research cost etc. However, there are no investigations on DOE in such a process. This investigation firstly tests the effects of three input variables, including tool rotation speed, feedrate, and ultrasonic power, on output variables, including cutting force, torque, and surface roughness, at two levels. This investigation will provide guides for future research.