The influence of beam intensity on laser ablation quality and ablation size is experimentally studied on graphene-coated silicon/silicon dioxide substrates. With an amplified femtosecond-pulsed laser system, by systematically decreasing the average power, periodic stripes with decreasing widths are ablated. Histogram analyses of the untouched and ablated regions of scanning electron microscope images of the fabricated structures make it possible to quantify the ablation quality. These analyses reveal that submicron ablation can be achieved while maintaining 75 % ablation accuracy by adjusting the beam intensity around the ablation threshold.