A scalable method for graphene and few-layer graphene (FLG) production by graphite delamination in aqueous solutions of the nonionic surfactant TWEEN^®80 (TW80) using stirred-media mills is presented. Delaminated product analysis using statistical Raman spectroscopy yielded extensive processing-structure-property relationships that revealed how stress intensity and specific energy input, i.e., the process parameters, govern the yield of graphene production and defect formation. The dispersed carbon concentration increased but the content and the quality of the FLG product decreased sharply with higher specific energy input. The FLG content of the product was up to 90%, especially for low specific energy input. Moreover, Raman analyses revealed that stress intensities greater than about 1 nJ were related to significant defect formation in the product particles. Another key parameter for graphene production is solvent viscosity. The FLG concentration in the product increased by a factor of 10 when the solvent's viscosity was increased from 1 to 6 mPa·s because shear- and friction-induced delamination was enhanced and in-plane fracture was reduced due to dampening of bead motion. Based on the processing-structure-property relationships found, we propose that the delamination process can be designed in such way that the product consists, almost totally, of FLG and that single-layer graphene is produced. The scalability of graphene production by stirred-media delamination was demonstrated when an increase in the batch size from 0.2 to 2 L had no significant effect on product quality.