Two new μ-oxamido-bridged dicopper(II) complexes formulated as [Cu₂(hmdoxd)(H₂O)(Me₂bpy)]-(ClO₄)·DMF (1) and [Cu₂(hmdoxd)(bpy)](ClO₄)·CH₃OH (2), where H₃hmdoxd is N-(2-hydroxy-5-methylphenyl)-N′-[2-(dimethylamino)ethyl]oxamide; Me₂bpy and bpy stand for 4,4′-dimethyl-2,2′-bipyridine and 2,2′-bipyridine, respectively, were synthesized and structurally characterized. The single-crystal X-ray diffraction analysis reveals that the copper(II) ions in complexes 1 and 2 are bridged by the cis-hmdoxd^3 − with corresponding Cu ⋯ Cu separations of 5.1596(6) and 5.1562(6) Å, respectively, in which the endo- and exo-copper(II) ions are located in square-planar and square-pyramidal geometries, respectively, for 1, and square-planar environments for 2. In the crystals of the two complexes, there are abundant hydrogen bonds and π–π stacking interactions contributing to the supramolecular structure. The DNA/protein-binding property of the two complexes are studied both theoretically and experimentally, indicating that complexes 1 and 2 can interact with DNA in the mode of intercalation and partial intercalation, respectively, and effectively bind to protein BSA via the favored binding sites Trp213 for 1 and Trp134 for 2. In vitro anticancer activities showed that the two complexes are active against the selected tumor cell lines, and the anticancer activities are consistent with their DNA/protein-binding affinities following the order of 1 > 2. The effect of the hydrophobicity of both the bridging and terminal ligands in the dicopper(II) complexes on DNA/protein-binding events and in vitro anticancer activities is preliminarily discussed.