Laser beam cutting of carbon fiber reinforced plastics has technical and economic potential due to its wear-free and force-free operation. However, the low technical processing quality, characterized by a heat-affected zone or low feed rates during cutting, hinders the establishment of the process. This work identifies the cause of the primary conflict between the average width of the heat-affected zone and the effective feed rate during cutting with multiple laser exposures. Based on this conflict, a process quality is defined, which is optimized through empirical and simulation methods. Additionally, a material modification is implemented to enhance the absorption of laser radiation. Furthermore, the material adaptation to the laser process, particularly the section-wise adjustment of process parameters, is investigated through numerical process simulation and optimization. A method for contactless measurement of the width of the heat-affected zone using thermography is also discussed. The approaches are demonstrated on an automotive component.