<p>Carbide circular saw blades are irreplaceable tools for cold-cutting processes. However, sawing force models related to the metal sawing process have not been reported. In this study, a theoretical model of dynamic sawing force is proposed which considers sawing geometry (sawing arc length, sawing parameters, etc.) and runout errors. The instantaneous undeformed chip thickness (IUCT) was obtained by the sawtooth elemental motion method to establish the dynamic sawing force model. The IUCT model is optimized considering the runout error of the optical measurements. Then, the proposed model is validated by sawing experiments with average errors of 8.25% and 3.03% for horizontal and vertical sawing forces, which demonstrates that the model can predict sawing forces accurately. The parameterization of the model shows that the sawing force is inversely proportional to the rotational speed and directly proportional to the feed rate and sawing depth. The results indicate that the saw teeth may not be involved in sawing due to runout errors. The model, leveraging the cutting force model, provides a solution for optimizing sawing parameters, designing circular saw blade dimensions, and even monitoring wear conditions. Hence, the proposed model can be extended to calculate the cost and energy consumption in the metal sawing industry.</p>