Two mononuclear copper (II) terpyridine complexes namely, [Cu(Btptpy) (ClO(4))](ClO(4)) 1, and [Cu(Bttpy) (ClO(4))](ClO(4)) 2, (Btptpy (L(1)) = 4'-(Benzothiophene)-2,2':6',2″-terpyridine, Bttpy (L(2)) = 4'-(Benzylthiazolyl)-2,2':6',2″-terpyridine) have been synthesized and characterized. Single crystal X-ray diffraction shows that, both ligands belong to monoclinic crystal system with space group P2(1)/c (L(1)) and P2(1)/n (L(2)). Absorption spectral titration, DNA melting study, circular dichroism and viscosity measurement reveal that, complex 1 and 2 bind with DNA through intercalation. In addition, interaction between the two copper (II) complexes and bovine serum albumin (BSA) has been studied by fluorescence titration, circular dichroism and their protease activity has been investigated using SDS-PAGE gel electrophoresis. Agarose (AGE) and SDS-PAGE gel electrophoresis reveals both complexes have good nucleolytic and proteolytic property in the presence of additive hydrogen peroxide. Both complexes shows remarkable cytotoxic property against triple negative CAL-51 human breast cancer cell line and hepatocellular carcinoma (HepG2) cancer cell lines and bears very less cytotoxicity towards liver normal cell line (Changs). DCF-DA and TBRAS assay also supported that complex 1 and 2 induces elevated level of reactive oxygen species (ROS) and oxidative stress in cancer cells than normal cell line. Furthermore, FACS analysis confirms complex 1 and 2 brings apoptosis by growth phase cell cycle arrest.