Background/Objectives: β-Lapachone (β-lap) is an o-naphthoquinone with potent antitumor activity. However, its clinical application is hindered by poor solubility and toxicity. Thiosemicarbazone derivatives of β-lap (BV3 and BV5) have demonstrated enhanced selectivity and anticancer efficacy in leukemia cells. Therefore, this study aimed to evaluate the therapeutic potential of these derivatives in solid tumors. Furthermore, the mechanism of tumor cell death, the involvement of protein kinase inhibition, and the toxicogenetic safety of BV3 and BV5 were investigated. Methods: The cytotoxic effects of BV3 and BV5 were assessed in cancer cell lines and a non-cancerous cell line. The compounds were most effective against HeLa (human cervical adenocarcinoma) cells. For that reason, this type of cell was chosen to study how the compounds might cause cell death, using flow cytometry. Kinase inhibition assays were conducted in vitro and in silico, followed by genotoxicity assessments to determine toxicogenetic safety. Results: BV3 and BV5 derivatives significantly inhibited cancer cell proliferation after 72 h, with IC₅₀ values ranging from 2.8 to 36.9 µM. BV3 demonstrated superior selectivity (selectivity index: 15.6) when compared to β-lap (selectivity index: 1.9) in HeLa cells. Morphological changes and flow cytometry analysis revealed features of apoptosis and/or necrosis in HeLa cells treated with the compounds BV3 and BV5. Furthermore, among the kinases tested, BV3 and BV5 were more effective in inhibiting the activity of the protein kinases JAK3 and GSK3β. This result was also confirmed by the in silico studies. Additionally, genotoxicity assays indicated an overall favorable toxicogenetic safety profile; however, BV5 exhibited potential genotoxicity at high concentrations. Conclusions: The findings underscore the anticancer potential of BV3 and BV5 in solid tumors and highlight their mechanism of action, which involves protein kinases. The findings also show that the drugs are selective and relatively safe.