<p>Cutting is an essential process in the manufacture of carbon-fiber-reinforced plastics (CFRPs), and predicting cutting forces plays a crucial role in cutting optimization. Specific cutting forces are paramount for the development of cutting force models. However, deriving specific cutting forces in CFRPs is a complex and challenging task. This study presents two novel methods for deriving specific cutting forces in CFRP cutting: the instantaneous chip-division method and the mechanistic model-based identification method. The instantaneous chip-division method allows for a detailed derivation of specific cutting forces at fine fiber cutting angle resolutions, whereas the mechanistic model-based identification method simplifies experimental procedures, but is limited in its analysis depth. Specific cutting forces derived by both methods were successfully regressed to sine functions and exhibited minor differences in phase and magnitude. A comparison of the predicted cutting forces with experimental data across various fiber orientation angles and radial depths of cut revealed the accuracy of both methods, with consistently low mean absolute percentage errors (&lt; 20%), with the exception of one condition. For a fiber orientation angle of 0°, the mechanistic model-based identification method exhibited relatively large errors. These specific cutting force derivation methods offer efficient tools for analyzing and predicting CFRP cutting forces, contributing to the optimization of cutting processes and the resolution of challenges in CFRP machining, thereby advancing this field.</p> Graphical Abstract <p></p>