Poor surface finish of as-built metal Additive Manufacturing (AM) remains a key challenge in fabricated parts. Metal AM parts typically require postprocessing to improve surface finish before application. Furthermore, different surface orientations and scanning strategies in Powder-Bed-Fusion (PBF) metal AM are prone to result in non-uniform surface roughness across different surfaces of a part. In recent years, Mass Finishing (MF) technologies, such as Centrifugal Disc Finishing (CDF), are gaining popularity in improving AM surfaces due to its fixture-free, batch-processing, and relatively low costs. There is a critical need to study the surface finish dependency on AM build orientation and MF processing conditions. In this study, Ti6Al4V ASTM-E8b tensile bars were fabricated in 45⁰ and 90⁰ orientation via Laser Powder Bed Fusion (L-PBF) to investigate the effects of CDF processing conditions on upward facing surface (up-skin), downward facing surface (down-skin), and side facing surface (side-skin). The surface roughness evolution on each type of surface were collected via laser scanning profilometry. It was found that both processing speed and processing time of CDF were statistically significant factors in improving AM surface roughness, however, processing time had higher impact. Furthermore, different build orientation demonstrated different surface roughness reduction rate and material removal rate. It was found that side-skin had the highest average roughness reduction, and the down-skin exhibited the least roughness reduction. In addition, this study found that the surface with the highest initial surface roughness (down-skin) had the least material removal rate, and that the highest material removal rate was observed in surface with higher periodicity (side-skin). Findings from this study will help the AM community in decision-making of CDF conditions to prevent over-finishing and under-finishing. In addition, the investigation of surface evolution dependency on AM build orientation can further improve the understanding of key mechanisms of AM + MF hybrid manufacturing system.