Two new dicopper(II) complexes bridged by N,N'-bis(dipropylenetriamine)oxamide (H2oxdipn), namely, Cu2(oxdipn)2(1) and [Cu2(oxdipn)(ClO4)2] (2), where pic represents picrate ion, have been synthesized and characterized by elemental analyses, molar conductance measurements, IR and electronic spectral studies, and X-ray single crystal diffraction. In both dicopper(II) complexes, the two copper(II) ions are bridged by trans-oxdipn ligand with the Cu⋯Cu separations of 5.2536(15) and 5.231(2)Å, respectively. The copper(II) ion in complex 1 has a square-planar coordination geometry, while that in 2, a square-pyramidal. Linked with classical hydrogen bonds, the molecules of complex 1 consist of a one-dimensional chain, while complex 2 molecules result in a two-dimensional structure. Numerous hydrogen bonds link complex 1 or 2 into a 2-D infinite network. In vitro cytotoxicity experiment shows that the two dicopper(II) complexes exhibit cytotoxic effects against the selected tumor cell lines. The reactivity towards herring sperm DNA (HS-DNA) and bovine serum albumin (BSA) reveals that the two dicopper(II) complexes can interact with the DNA in the mode of intercalation, and effectively quench the intrinsic fluorescence of BSA via a static mechanism. The influence of different counterions in this kind of dicopper(II) complexes on DNA/BSA-binding properties, and the in vitro cytotoxic activities was investigated.