Cancer therapy is one of the most important challenges of modern medical and chemical sciences. Among the many methods of combating cancer, chemotherapy plays a special role. Imperfect modern chemotherapy justifies continuing the search for new, more effective, and safe drugs. Sulfonamides are the classic group of chemotherapeutic drugs with a broad spectrum of pharmacological activity. Recent literature reports show that sulfonamide derivatives have anti-tumor activity in vitro and in vivo. The aim of the study was to synthesize a novel 1,2,4-triazine sulfonamide derivative and check its anticancer potential in DLD-1 and HT-29 colon cancer cells. The biological studies included MTT assay, DNA biosynthesis, cell cycle analysis, Annexin V binding assay, ethidium bromide/acridine orange staining, and caspase-8, -9, and -3/7 activity. The concentrations of important molecules (sICAM-1, mTOR, Beclin-1, cathepsin B) involved in the pathogenesis and poor prognosis of colorectal cancer were also evaluated by ELISA. We demonstrated that the novel compound was able to induce apoptosis through intrinsic and extrinsic pathways and was capable of decreasing sICAM-1, mTOR, cathepsin B concentrations, whereas increased Beclin-1 concentration was detected in both colon cancer cell lines. The novel compound represents promising multi-targeted potential in colorectal cancer, but further in vivo examinations are needed to confirm the claim.