In this work, we synthesized a novel, free-standing, flexible sodium-bentonite-fabricated graphene (SBG) composite membrane. The prepared SBG membrane was successfully employed for the selective separation of oil and water. SBG-fabricated filter paper and cotton cloth membranes were easily prepared using simple vacuum filtration and coating methods. The SBG composite membrane exhibited switchable wettability properties, which rendered it capable of switching the surface into either hydrophilic/oleophobic or hydrophobic/oleophilic with the selective treatment of water or oil/organic solvent, respectively. The prepared SBG composite was characterized using X-ray diffraction, thermo-gravimetric analysis, X-ray photoelectron spectroscopy and scanning electron microscopy. The as-prepared membrane has high efficiency (>98%) to separate oil–water mixtures, a good recyclability (96% efficiency after 10 cycles), a high flux of 625 Lm⁻²h⁻¹, and a good oil rejection ratio (>97%). The SBG composite can easily be scaled to separate the oil–water mixture for industrial applications. Furthermore, the advantages of the membrane are its easy preparation, self-cleaning property, switchable wettability property (hydrophilic/oleophobic to hydrophobic/oleophilic and vice versa), high flux and excellent recyclability for the selective separation of oil/organic solvents and water from their mixtures.