This research investigated the effect of tool geometry, rotation, and advancing speed on the microstructure and mechanical properties of aluminum AA6061-T6/graphene nanocomposites fabricated by friction stir processing (FSP) using three conical tools with the pin cone angles (PCAs) of 2, 2.5, and 3°. In the first step of the study, the process was performed with and without graphene nanoplatelets (GNPs) at different rotations (710, 1120, and 1400 rpm) and advancing speeds (80, 125, and 160 mm/min). The yield strength, tensile strength, and microhardness of all the samples were lower than those of the base metal. In the second step of the study, the heat input was controlled by reducing rotations (112, 180, and 280 rpm) and advancing speeds (31.5, 25, and 20 mm/min). The mechanical properties of processed samples were studied by tensile tests and microhardness measurements. Microstructural evolution in samples was analyzed by means of a field emission scanning electron microscope (FESEM) equipped with an X-ray energy dispersive spectrometer (EDS) and electron back-scattered diffraction (EBSD) detector. The results indicated that the mechanical properties were improved in the second step with the increase in the advance per revolution (APR) and the PCA. This was linked to the microstructure evolution in the processed samples affected by process parameters and regulated heat input. The effect of each input variable on the mechanical properties was evaluated by statistical analysis and was validated by analysis of variance (ANOVA). The optimal processing was attained by utilization of PCA, tool rotation, and advancing speed.