To improve soil clod removal and reduce potato damage in potato combine harvesters, this study investigates the processes involved in soil clod removal and potato collisions within the bar-lift chain separation device of the harvester. It outlines the structure and working principles of the machine, theoretically analyzes the key dimensions of the digging device and potato–soil separation components, and derives specific structural parameters. A dynamic mathematical model of the bar-lift chain is established, from which the dynamic equations are formulated. The analysis identifies factors that influence the dynamic characteristics of the bar-lift chain. This study examines the working principles and separation performance of the potato–soil separation device, with a focus on the collision characteristics between potatoes and both the screen surface and the bars. Key factors such as the separation screen’s line speed, the harvester’s forward speed, and the tilt angle of the separation screen are considered. Simulations are performed using a coupling method based on the Discrete Element Method (DEM) and Multi-Body Dynamics (MBD). Through simulation experiments, the optimal parameter combinations for the potato–soil separation device are determined. The optimal working parameters are identified as a separation screen line speed of 1.25 m/s, a forward speed of 0.83 m/s, and a tilt angle of 25°. Field harvesting experiments indicate a potato loss rate of 1.8%, a damage rate of 1.2%, an impurity rate of 1.9%, a skin breakage rate of 2.1%, and a yield of 0.15–0.21 ha/h. All results meet national and industry standards. The findings of this research provide valuable theoretical references for simulating potato–soil separation in combine harvesters and optimizing the parameters of these devices. Future potential research will consider the automatic regulation of the excavation volume of the potato–soil mixture, aiming to achieve intelligent control of the potato–soil separation operation.