<p>This paper focuses on the study of a vertical spiral stirred mill, thoroughly analyzing the dynamic behavior of the grinding media within the mill barrel, aiming to achieve a comprehensive understanding of the internal operating mechanisms of this type of equipment. Firstly, based on the working principles of the vertical spiral stirred mill, a discrete element method (DEM) simulation model was constructed, and its validity was verified through experiments. Then, to explore the kinematic characteristics of the grinding media in multi-dimensional space, a refined velocity model of the grinding media was developed using vector decomposition techniques. On this basis, key control parameters such as the pitch of the spiral agitator, blade diameter, rotation speed, and grinding media filling were systematically analyzed for their effects on the motion patterns of the grinding media, relying on the validated DEM model. The results indicate that in the axial dimension, the axial velocity of the grinding media, along with the circumferential velocity in the central region of the mill, exhibits high stability, revealing the uniformity of the motion state in this region. Simultaneously, in the radial region between the outer edge of the spiral blades and the mill wall, the grinding media present significant gradients in both circumferential and axial velocities, indicating this area as a crucial grinding zone. Further analysis shows that the pitch of the spiral agitator, blade diameter, and rotation speed significantly affect the circumferential velocity in the radial direction, while both blade diameter and rotation speed also play a dominant role in the axial velocity. In contrast, the filling of the grinding media has a minimal effect on the overall motion patterns, suggesting that the dynamic characteristics of the grinding media are primarily influenced by the mechanical structure design and operational parameters.</p>