A novel series of N-substituted isatin thiosemicarbazone ligands (L1–L3) and their copper(II) complexes [Cu(II)(ITSC)] were synthesized and characterized by elemental analyses and UV–Vis, FT-IR, 1H &13C NMR/EPR and mass spectroscopic techniques. The molecular structures of L1, L2, L3, 2 and 3 were confirmed by single crystal X-ray crystallography. The X-ray diffraction studies of the complexes 2 and 3 reveal the square planar and square pyramidal geometry. The binding affinity and binding mode of the monometallic and bimetallic complex toward calf thymus DNA (CT-DNA) and bovine serum albumin (BSA) were determined by UV–Vis and fluorescence spectrophotometric methods. Spectral evidences show intercalative mode of DNA binding with the copper(II) complexes. Complexes (1, 2 and 3) cleaved the pUC19 plasmid DNA in the absence of an external agent. An in vitro cytotoxicity study of the complex 3 found good activity against human breast (MCF7) and lung (A549) cancer cell lines.