To realize a one-sided stitching action and stable stitch formation, a poor match between the lead and the hook yarn needles in the stitching process must be avoided as it can lead to hook dropping and hook errors, causing loop loss, thread breaking, and even thread relaxing. Based on an analysis of the principle of one-sided stitching and matching the hook and lead yarn needles, the original stitching technology is improved and a method of trajectory superposition is proposed. A yarn-pulling mechanism is designed for a one-sided stitching device for three-dimensional preformed carbon/carbon composites. By analyzing the principle of the yarn-pulling mechanism, a mathematical model of that mechanism is established, and a trajectory simulation analysis is carried out with MATLAB, which verifies the rationality of the yarn-pulling principle. Results for the two crank angles of the yarn-pulling mechanism and the crank angle of the hook yarn needle at two particular moments reflect the matching relationship of the three, which provides a theoretical reference for the stitching device to adjust to and work well, forming the desired stitch. Finally, stitching tests are carried out, and the test results show the designed yarn-pulling mechanism can cooperate with the hook and the lead yarn needles to complete the stitch lock. This realizes a stable stitching action and avoids hook dropping and hook errors, thereby increasing stitching efficiency.