Copper-based artificial metallonucleases are likely to satisfy more biomedical requirements if their DNA cleavage efficiency and selectivity could be further improved. In this study, two copper(II) complexes, [CuL(1)Cl(2)] (1) and [CuL(2)Cl(2)] (2), and two copper(II)-platinum(II) heteronuclear complexes, [CuPtL(1)(DMSO)Cl(4)] (3) and [CuPtL(2)(DMSO)Cl(4)] (4), were synthesized using two bifunctional ligands, N-[4-(2-pyridylmethoxy)benzyl]-N,N-bis(2-pyridylmethyl)amine (L(1)) and N-[3-(2-pyridylmethoxy)benzyl]-N,N-bis(2-pyridylmethyl)amine (L(2)). These complexes have been characterized by elemental analysis, electrospray ionization mass spectrometry, IR spectroscopy, and UV-vis spectroscopy. The DNA binding ability of these complexes follows an order of 1 < 2 < 3 < 4, as revealed by the results of spectroscopy and agarose gel electrophoresis studies. Their cleavage activity toward supercoiled pUC19 plasmid DNA is prominent at micromolar concentration levels in the presence of ascorbic acid. The introduction of a platinum(II) center to the copper(II) complexes induces a significant enhancement in cleavage activity as compared with copper(II) complexes alone. These results show that the presence of a platinum(II) center in copper(II) complexes strengthens both their DNA binding ability and DNA cleavage efficiency.