A series of novel 4-alkylthio-2-chloro-5-[(2-arylmethylidene)hydrazinecarbonyl]benzenesulfonamide derivatives 3–22 were synthesized and evaluated for their inhibitory activity against human carbonic anhydrase isozymes hCA I, hCA II, hCA IX, and hCA XII. These compounds showed varying degrees of activity against the studied isoenzymes. However, the importance of substituent choice in designing potent carbonic anhydrase inhibitors is highlighted by the strong inhibition profiles of compounds 3 and 10 against hCA IX and the low average KI values for compounds 9 and 10 (134 nM and 77 nM, respectively). All the synthesized compounds were evaluated for their antiproliferative activity toward HeLa, HCT-116, and MCF-7 cell lines. Compounds 9 and 19 exhibited significant activity, particularly against the MCF-7 cell line (IC50 values of 4 μM and 6 μM, respectively). Notably, compound 9 demonstrated a high selectivity index (SI = 8.2) for MCF-7 cells. The antiproliferative effects of compounds 9 and 19 were linked to the induction of cell cycle arrest and apoptosis via the mitochondrial pathway and involved the activation of the MAPK/ERK signaling pathway. Inhibition of MAPK/ERK activity reduced the compounds’ ability to induce cell cycle arrest and apoptosis, indicating the critical role of this pathway. These findings suggest that compounds 9 and 19 are promising candidates for further development as specific and potent anticancer agents targeting the MAPK/ERK pathway.