Ceramic structural parts are one of the most widely utilized structural parts in the industry. However, they usually contain defects following the pressing process, such as burrs. Therefore, additional trimming is usually required, despite the deformation challenges and difficulty in positioning. This paper proposes an ultrafast laser processing system for trimming complex ceramic structural parts. Opto-electromechanical cooperative control software is developed to control the laser processing system. The trimming problem of the ceramic cores used in aero engines is studied. The regional registration method is introduced based on the iterative closest point algorithm to register the path extracted from the computer-aided design model with the deformed ceramic core. A zonal and layering processing method for three-dimensional contours on complex surfaces is proposed to generate the working data of high-speed scanning galvanometer and the computer numerical control machine tool, respectively. The results show that the laser system and the method proposed in this paper are suitable for trimming complex non-datum parts such as ceramic cores. Compared with the results of manual trimming, the method proposed in this paper has higher accuracy, efficiency, and yield. The method mentioned above has been used in practical application with satisfactory results.