Functionalized graphene oxide (GO) nanoparticles are being increasingly employed for designing modern drug delivery systems because of their high degree of functionalization, high surface area with exceptional loading capacity, and tunable dimensions. With intelligent controlled release and gene silencing capability, GO is an effective nanocarrier that permits the targeted delivery of small drug molecules, antibodies, nucleic acids, and peptides to the liquid or solid tumor sites. However, the toxicity and biocompatibility of GO-based formulations should be evaluated, as these nanomaterials may introduce aggregations or may accumulate in normal tissues while targeting tumors or malignant cells. These side effects may potentially be impacted by the dosage, exposure time, flake size, shape, functional groups, and surface charges. In this review, the strategies to deliver the nucleic acid via the functionalization of GO flakes are summarized to describe the specific targeting of liquid and solid breast tumors. In addition, we describe the current approaches aimed at optimizing the controlled release towards a reduction in GO accumulation in non-specific tissues in terms of the cytotoxicity while maximizing the drug efficacy. Finally, the challenges and future research perspectives are briefly discussed.