A heat-affected zone significantly reduces the mechanical properties of carbon fiber-reinforced plastics (CFRP). However, the beam quality, especially the stability of the beam pointing, limits the heat-affected zone (HAZ) minimization studies. In this study, the HAZ is reduced by improving the pointing stability of the laser beam. A beam pointing stabilization system (BPSS) based on position-sensitive devices and fast steering mirrors (FSMs) was developed. The research focuses on building a control model from the position-sensitive devices’ position deviation signals to the FSMs’ corrected control angles. The control model can detect and predict the beam pointing deviations and correct the attitudes of the FSMs to correct the beam pointing deviations, improving the beam pointing stability. The performance of the proposed BPSS and the corresponding control model were experimentally verified. The results indicate that the pointing deviations of the corrected beam in the X and Y directions are reduced by 78.08% and 70.28%, respectively. Additionally, the HAZ of CFRP processed with the corrected laser is reduced by 30.8%. The quality of the laser cutting of CFRP is significantly improved.