The reaction of substituted acylthiourea derivatives (L1–L4) with [(PPh3)2Cu(μ-Cl)2Cu(PPh3)] in a proper stoichiometric proportion gave the complexes (1–4) in good yields. The structures of the compounds (ligands and complexes) were advocated through spectroscopic analyses and x-ray diffraction (XRD) studies; the latter confirmed their molecular structures. The complexes (1–4) were assessed for their cytotoxic potential through MTT assay against A549, T24, and HepG2 cancer cells, and their toxicity was evaluated using Vero and MCF-10a normal cells. The complexes (1–4) displayed better cytotoxic action toward HepG2 cancer cells than cisplatin. Complexes 3 and 4 significantly destroyed A549 cancer cells with the IC50 values of 16.25 and 4.90 μM, respectively, which were lower than that of cisplatin (IC50 = 17.73 μM). Furthermore, the higher IC50 values in normal cells showed that the complexes were less hazardous to the normal cells except complex 3. The biocompatibility study showed that the complexes had minimal impact on normal human dermal fibroblast (NHDF) cells. The mode of cell death of complexes 3 and 4 against cancer cells was evaluated using staining assays. Both compounds demonstrated a significant reduction in live cells, an increase in early apoptotic cells, and pronounced proapoptotic effects, as evidenced by fragmented nuclei. Flow cytometry revealed a distinctive subpopulation in the subG0 phase, highlighting the compounds' ability to induce apoptosis and inhibit cell cycle progression.