In this paper, we present for the first time the evaluation of cytotoxicity and genotoxicity of de novo synthesized pyrazolo[4,3-e]tetrazolo[1,5-b][1,2,4]triazine sulfonamides MM129, MM130, and MM131 in human tumor cell lines: HeLa, HCT 116, PC-3, and BxPC-3. Cytotoxic and genotoxic properties of the tested compounds were estimated using the MTT assay, comet assay (alkaline and neutral version), and γ-H2AX immuno-staining. Examined sulfonamides exhibited strong anticancer properties towards tested cells in a very low concentration range (IC50 = 0.17–1.15 μM) after 72 h exposure time. The results of the alkaline and neutral version of the comet assay following 24 h incubation of the cells with tested compounds demonstrated the capability of heterocycles to induce significant DNA damage in exposed cells. HCT 116 cells were the most sensitive to the genotoxic activity of novel tricyclic pyrazolo[4,3-e]tetrazolo[1,5-b][1,2,4]triazine sulfonamides in the neutral version of the comet assay. Immunocytochemical detection of γ-H2AX showed an increase in DNA DSBs level in the HCT 116 cell line, after 24 h incubation with all tested compounds, confirming the results obtained in the neutral comet assay. Among all investigated compounds, MM131 showed the strongest cytotoxic and genotoxic activity toward all tested cell types. In conclusion, our results suggest that MM129, MM130, and MM131 exhibit high cytotoxic and genotoxic potential in vitro, especially towards the colorectal cancer cell line HCT 116. However, further investigations and analyses are required for their future implementation in the field of medicine.