The aim of this study is to focus on the multiresponse-process optimization of friction stir processing of AA6063/$n$-graphene-based surface composites to obtain enhanced mechanical properties using Taguchi’s technique combined with grey relational analysis (GRA) technique. The parameters of the process selected for this study are tool rotation speed (rpm), tool traverse speed (mm/min), and tilt angle (°). Commonly followed mechanical characterization, namely, hardness and tensile strength are considered as the output performances. The experiments are conducted with a minimal run designed by Taguchi’s $L_{9}$ orthogonal array factorial design of experiments. GRA is used to optimize the multiresponse-process parameters. In accordance with the analysis, it is found that the specimen synthesized with the tool rotation speed of 1200 rpm, traverse speed of 40 mm/min, and 1.5° tilt angle exhibits superior mechanical properties. Analysis of the variance is done to study the dominant factor affecting the strength of the processed composites. SEM analysis with EDX spectrum is done to study the morphological characterization of the prepared composites.