When a CFRP (Carbon Fiber Reinforced Plastics) plate, which is light weight and high strength composite material, is machined with a cutting tool, the surface integrity depends on the cutting direction with respect to the fiber orientation. The cutting tests were conducted in planning of unidirectional CFRPs with a single crystal diamond tool at a cutting speed of 100 mm/min in a depth of cut of 75 μm. In this study, "the cutting direction angle" is defined as the relative angle of the cutting direction with respect to the fiber orientation. The cutting forces and the surface finishes are investigated at cutting direction angles of 0, 45 and 90 degrees. The surface is finished without damages in subsurface at a cutting direction angle of 0 degree. Meanwhile, the huge delamination on the surface and the large damages in the subsurface occur with cutting of fibers and pulling of matrix at a cutting direction angle of 90 degrees. The breakage of the fibers and the delamination induce vibrations in the cutting forces at cutting direction angles of 0 and 90 degrees.