With the carbon fiber reinforced resin matrix composite (CFRP) as the processing object, the thermal damage inhibition experiment was carried out around the improvement of 1 064 nm picosecond laser processing mode and the adjustment of process parameters. The results show that the cutting quality along the fiber direction is better than that in the vertical direction, and the anisotropy of the material determines that the heat mainly transfers along the fiber direction and diffuses to the inside of the material. The composite cutting method of moving platform combined with galvanometer is better than the traditional method, and is suitable for thick material processing. The degree of thermal damage is closely related to laser power, cutting speed, scanning radius and filling distance, which is determined by pulse energy density and pulse dispersion. In addition, cutting quality can be further improved by properly increasing cutting times after cutting through materials. After the process optimization, the cutting quality of 2.1 mm thick sample is excellent by composite method, and excellent cutting quality was obtained. There were no defects such as attachments, cracks and pores on the surface of the slit, and the width of the heat affected zone in the material was less than 10 μm.