Free standing 3D graphene nanoedges with a high surface area, density of armchair oriented graphene edges, crystallinity and thermal stability in air was scalably produced via the electrolytic exfoliation of graphite in molten NaCl-LiCl, and the performance of this material as an effective adsorbent for removal of methyl orange (MO) from aqueous solutions was comprehensively evaluated. The graphene material before and after being used in the adsorption process was characterized by various techniques including electron microscopy, X-ray diffraction (XRD) and Raman and FTIR analysis. High resolution TEM examination of the graphene nanoedges demonstrated the presence of a high fraction of single-, double- and few-layer graphene nanosheets together with graphitic layers with a thickness of < 10 nm. The graphene material exhibited an excellent MO absorption capability at a wide pH range from 2 to 11. The presence of the pi - pi interaction and hydrogen bonds between the MO and graphene edges were found to be responsible for the high MO adsorption. Three kinetic models; Frendluich, Temkin and Langmuir, were employed to evaluate the experimental equilibrium data, and the latter provided the best fit to the adsorption process, based on which the monolayer sorption capacity was found to be 27.932 mg/g. The electrolytic 3D graphene possesses an impressive thermal stability in air up to about 500 degrees C. Based on this, a simple, cost-effective and ultra-scalable thermal treatment was employed for the regeneration of the adsorbent, resulted in an efficient recovery of the 3D geraphene. Moreover, the regenerated adsorbent exhibited a remarkable absorption performance. These characteristics make the molten salt graphene an interesting candidate as an economic and efficient adsorbent for the treatment of wastewaters.