The cleaning system is a critical component of the sugarcane chopper harvester, facing challenges such as high impurity rate, elevated power consumption, and an inadequate understanding of the cleaning mechanism. This study aims to simulate the process of removing extraneous matter (represented by sugarcane leaves) from the cleaning system by employing a coupling approach of computational fluid dynamics (CFD) and the discrete element method (DEM) to determine the speed of the extractor fan. Initially, a CFD model was established to analyze the airflow field within the extractor, and its accuracy was verified on a test bench for the cleaning system. Subsequently, a DEM model was developed for sugarcane billets and leaves, which was then integrated with the CFD model to form a gas–solid coupling model. The efficacy of this integrated model was confirmed through experimental measurements of impurity rate. Furthermore, a ternary quadratic regression orthogonal combination design was utilized in the gas–solid coupling simulation to assess the impacts of feed rate, leaf–stalk ratio, and extractor fan speed on impurity rate. Finally, the extractor fan speeds were obtained for various feed rates and leaf–stalk ratios under impurity rates of 5%, 6%, 7%, and 8%. This research can guide in controlling the extractor fan speed during sugarcane chopper harvester field operations and can serve as a foundation for extractor fan design.