Sawing by circular saw blades is predominant in the mechanized treatment of natural stone. The predictive sawing force is crucial for optimizing, controlling, and monitoring the sawing process. In this work, a novel model for predicting sawing force, which is based on the distribution of the undeformed chip thickness at the sawing contact arc, was proposed. Based on the analysis of the undeformed chip geometry of the circular saw blade, the segment surface was divided into the front end and rear end according to the contact pattern between the segments and granite, and the models of the maximum undeformed chip thickness of diamond particles on the front end and rear end were established. Results showed that the new proposed force model fully considered the distribution of undeformed chips compared with the current model. The novel model has higher prediction accuracy, the mean maximum absolute error is within 3.77%, and the maximum absolute error is within 7.83%. Through theoretical analysis, the ratio of the maximum undeformed chip thickness of the front segment to the rear segment is 1.67, which can fully explain the wear non-uniformity of the segment. The proposed model is of great significance to the optimization of the saw blade structure and process parameters.