The feeding sagittal angle of the forage harvester has a significant impact on the torque load and cutting performance of the cutting roller. By detecting the relationship between the transmission belt pressure and the feeding sagittal angle of the crop, kinematic and dynamic analysis was conducted on the cutting characteristics of the harvester and the crop cutting process. The relationship between the cutting quality, energy consumption, and the feeding sagittal angle of the forage crop was revealed. A mathematical model for the feeding sagittal angle of the harvester’s cutting roller was established and optimized. The experimental results showed that when the crop feeding amount in the optimized parameter group was 5.5kg/s, the cutting roller speed was 1600r/min, and the initial pressure of the transmission belt was 1.2MPa, the mathematical model accuracy of the cutting crop feeding sagittal angle under this operation parameter group was the highest, with an accuracy of 79.52% and a model deviation of 0.491MPa (0.957rad), which can effectively represent the cutting load of the hay cutter. At the same time, the cutting ability of the hay cutter was improved while ensuring the quality of crop cutting. Under the optimized cutting feeding sagittal angle model, the cutting disturbance response time was shortened by about 26.41%, and the unit operation energy consumption was reduced by about 11.36%. The establishment of the sagittal angle model for feeding the chopped crops enriched the modeling method for the cutting operation of the hay cutter, providing a reference for the design of the load control system of the hay cutter for similar forage crops.