Cutting edge preparation is a precision machining process that improves the surface quality of cutting tools through the relative movement of abrasives and the tool. Research on removing materials in drag finishing can be greatly beneficial to tool manufacturing. This paper proposes the hypothesis that both abrasive wear and erosion wear act on the surface of milling tools and discusses the material removal models for abrasive wear and erosion wear. The influence of immersion depth, abrasive velocity, abrasive radius, and abrasive density on the material removal rate in two material removal forms is compared and validated by discrete element simulations. The results show that immersion depth has a greater impact on abrasive wear, while abrasive properties have a greater impact on erosion wear. The correlation between simulation results and theoretical models demonstrates the sensitivity of the two forms of wear on this surface to parameter change differences. Dragging finishing was conducted to verify the effectiveness of the simulation, and the effects of immersion depth, dragging velocity, and abrasive properties on the edge radius and form factor (K value) were studied.