High-precision control of the dispersion of aggregates in a stirred media mill requires a thorough understanding of the motion of multiphase flows. Here, we present numerical methods to study the dispersion mechanism and estimate the impact and fluid shear powers arising in such a mill. Volume-averaged four-way coupling equations are used to simulate the bead motion and turbulent flow: a distinct element method (DEM) is employed for simulating bead motion, while large eddy simulation (LES) is used for simulating turbulence. The simulated particle and fluid velocities are in good agreement with the experimental findings at various stirring rates, showing the reliability of the DEM-LES method. Next, methods to calculate the powers of fluid shear, bead collision, and friction are presented. These methods are used to study the effect of each type of power on the dispersion process at various bead filling ratios. An increase in the filling ratio from 0 to 50 vol% causes a dramatic increase in the power of the fluid shear of pore fluid flow within the beads and a similar increase in the collision and friction powers. Further increase in the filling ratio to 83 vol% results in only a slight decrease in the collision and friction powers. However, the associated increase in the total bead-bead contact area leads to an increase in the effect of these powers on dispersion. The fluid shear power dominates the initial stage of the dispersion, whereas the collision and friction powers are dominant during the subsequent gradual dispersion process.