The increasing rate of oral squamous cell carcinoma (OSCC) and the undesirable side effects of anticancer agents have enhanced the demand for the development of efficient, detectable, and targeted anticancer systems. Saponins are a diverse family of natural glycosides that have recently been evaluated as an effective compound for the targeted therapy of squamous cell carcinoma. Due to their porous nature and stable structure, metal–organic frameworks (MOFs) are a well-known substance form for various biological applications, such as drug delivery. In this study, we fabricated a novel hybrid, highly porous and low-toxic saponin-loaded nanostructure by modifying graphene oxide (GO)/reduced GO (rGO) with aluminum fumarate (AlFu) as MOF core–shell nanocomposite. The characterization of the nanostructures was investigated by FTIR, TEM, EDX, FESEM, and BET. MTT assay was used to investigate the anticancer activity of these compounds on OSCC and PDL normal dental cells. The effect of the nanocomposites on OSCC was then investigated by studying apoptosis and necrosis using flow cytometry. The GO/rGO was decorated with a saponin–AlFu mixture to further investigate cytotoxicity. The results of the MTT assay showed that PDL cells treated with AlFu–GO–saponin at a concentration of 250 μg/mL had a viability of 74.46 ± 16.02%, while OSCC cells treated with this sample at a similar concentration had a viability of only 38.35 ± 19.9%. The anticancer effect of this nanostructure on OSCC was clearly demonstrated. Moreover, the number of apoptotic cells in the AlFu–GO–saponin and AlFu–rGO–saponin groups was 10.98 ± 2.36%–26.90 ± 3.24% and 15.9 ± 4.08%–29.88 ± 0.41%, respectively, compared with 2.52 ± 0.78%–1.31 ± 0.62% in the untreated group. This significant increase in apoptotic effect observed with AlFu–rGO–saponin was also reflected in the significant anticancer effect of saponin-loaded nanostructures. Therefore, this study suggests that an effective saponin delivery system protocol for the precise design and fabrication of anticancer nanostructures for OSCC therapy should be performed prior to in vivo evaluations.