Abrasive processes represent the main methods for obtaining high-quality surface finish in metal parts. As one main characteristic, these processes have a relatively high consumption of energy per material volume removed, as well as many inputs, such as abrasive tools and equipment, and, consequently, a high associated environmental impact. Additive manufacturing is becoming a competitive method to produce customized parts, but the surface finish is often not good enough for the application, and post-processing is needed. In this work, a mass finishing process using a planetary mill with abrasive media made of sustainable materials (pecan nutshells) was used on AISI 316L stainless steel samples manufactured by selective laser melting (SLM). The main goal was to perform a multicriteria analysis of the sample surface before and after post-processing. Through the analysis, it could be observed that the nutshell abrasive media has results close to those of traditional ceramic media. The increase in the rotation speed of the planetary mill, increase of finishing time, and use of abrasive pastes can further increase the effectiveness of the process.