Graphene quantum dots (GQDs) are very precious, widely used, and face significant challenges in preparation methods. In this study, three mechanical methods are investigated for the preparation of GQDs. All of these methods are green, cost-effective, and simple. In fact, Graphite, as a main source of GQDs, is exfoliated and fragmented under mechanical forces by sonication and ball milling. This mechanical exfoliation method is effective for converting large flakes of graphite into quantum dots. Additionally, the proposed methods are simple and faster than other top-down GQD fabrication methods. High-power sonication is applied to graphene flakes by using the liquid-phase exfoliation method. The liquid phase consists of ethanol and water, which are completely eco-friendly. Exfoliation and fragmentation of graphene flakes are performed using different sonication and ball-milling times. The obtained results from the analysis of the synthesized GQDs exhibit pristine graphene's distinct structural, chemical, and optical properties. Several analyses, such as X-ray diffraction (XRD) and Fourier transform infrared spectroscopy, were applied to study the product structure. Dynamic light scattering (DLS) and field emission scanning electron microscopy (FESEM) were used to examine product size and morphology, which confirmed the nanosize of GQDs. The smallest observed size of GQDs is approximately 23 nm. It is estimated that 95% of the nanoparticles are between 0.001 and 0.1 μm in size (41 nm). The optical properties of GQDs were investigated by using ultraviolet-visible and photoluminescence (PL) techniques. The PL peak wavelength is approximately 610 nm. Eventually, the results proved that the combined use of two methods, ultrasonication and ball milling during liquid-phase exfoliation, will be a simple, cheap, and suitable method for the production of GQDs.