A series of six new bis(thiosemicarbazone)copper(I) complexes of the type [Cu(L1–6)2Cl] (1–6) have been synthesized and characterized. The molecular structure of the ligand L4 was determined by the single crystal XRD method. All the complexes adopted trigonal planar (Y-shaped) geometry. All the complexes strongly bind with CT-DNA via intercalative mode, which was further supported by molecular docking studies. Further, the complexes were effectively bind with BSA as observed by UV-Vis and fluorescence spectra. All the complexes effectively cleave pBR322 DNA through hydrolytic pathway as evidenced from T4 ligase experiments. All the complexes interact with the anticancer receptor focal adhesion kinase (FAK) via electrostatic, van der Waals, hydrogen bonding, σ–π and π–π interactions. In vitro cytotoxicity of the complexes were assessed by MTT assay against four cancer cell lines such as human breast adenocarcinoma (MCF-7), cervical (HeLa), epithelioma (Hep-2) and Ehrlich ascites carcinoma (EAC), and two normal cell lines namely normal human dermal fibroblasts (NHDF) and L6 myotubes with respect to the commercially used anticancer drug cisplatin. All the complexes induce apoptosis in EAC cells, which was confirmed by AO/EB, Hoechst 33258 and PI staining methods. The complexes block cell cycle progression of EAC cells in S phase (DNA synthesis). The cellular uptake studies confirmed the ability of the complexes to go into the cytoplasm and accumulation in the cell nuclei. In the in vivo anticancer studies, the complexes significantly reduce the tumour volume in female Swiss albino mice. Overall, our results ensure the role of thiosemicarbazone-based copper(I) complexes as prospective anticancer agents, induction of apoptosis and S phase arrest with the mitochondrial controlled pathway.