Additive manufacturing, particularly Fused Deposition Modeling (FDM), has profoundly impacted the production of polymer parts due to its flexibility and cost-effectiveness. However, a significant limitation of FDM printed parts is their elevated surface roughness, which can negatively affect their mechanical performance, fatigue resistance, and dimensional accuracy. This research aims to analytically and numerically investigate the impact of surface roughness on the mechanical behavior of FDM printed PLA parts. To this end, the study will compare as-printed surfaces with milled surfaces. The study emphasizes the importance of incorporating real surface roughness data into Finite Element Method (FEM) simulations to more accurately predict the mechanical behavior of the parts. Milling has been demonstrated to reduce surface roughness, thus improving the mechanical behavior of the parts. This is a critical factor in engineering applications, particularly those concerned with ensuring structural integrity. Based on the results obtained, it can be concluded that using a high cutting speed (100 m/min) in the milling process significantly improves the surface quality of printed PLA parts. Milling with high cutting speeds improves surface roughness and eliminates burr formation. The results also indicate that the high feed rate increases the rate of chip removal. This facilitated heat dissipation and reduced surface damage.