Nanocomposite-modified structures based on reduced graphene oxide (rGO) are preferred because of their excellent advantages. Here we assessed the comparative interaction of graphene oxide (GO), chemically reduced GO (rGO), copper and nickel spinel ferrite nanoparticles (CuFe2O4 NPs and NiFe2O4 NPs) and their nanocomposites with reduced graphene oxide (rGO[sbnd]CuFe2O4, rGO[sbnd]NiFe2O4 NCs). The synthesized nanomaterials were characterized by X-ray diffraction (XRD) and transmission electron microscope (TEM) analysis. The cytotoxic analysis revealed a nontoxic behavior at concentrations below 50 µg/mL in human fetal lung fibroblast (MRC-5), human hepatocellular carcinoma (HepG2), and human glioblastoma (TG98) cell lines. The IC50 values were found to be lower in rGO than that of GO in MRC-5 and T98G cell lines. 50 µg/mL and higher concentrations of rGO[sbnd]CuFe2O4 NCs displayed more potent cytotoxic effects in MRC-5 and HepG2 cell lines compared with the CuFe2O4 NPs. Cytotoxicity was decreased in HepG2 and T98G cell lines treated with rGO[sbnd]NiFe2O4 NCs compared to NiFe2O4 NPs but increased in MRC-5. According to the molecular docking results, DNA binding modes of all nanomaterials were found to be minor groove recognition, while their DNA binding affinities ranged between -4.78 and -12.89 kcal/mol. Docking results showed that, based on their sharp-edged conformations, GO and rGO, and rGO-MFe2O4 (M: Cu, Ni) composites may be promising shape-selective DNA minor groove binders, with the potential to cause specific DNA damage in cancer cells.