Two new dicopper(II) complexes bridged by asymmetric N,N′-bis(substituted)oxamide ligands: N-(5-chloro-2-hydroxyphenyl)-N′-[3-(2-hydroxyethylamino)propyl]oxamide (H3chpoxd) and N-(5-chloro-2-hydroxyphenyl)-N′-[(methylamino)propyl]oxamide (H3chmpoxd), and end-capped with 2,2′-bipyridine (bpy), namely [Cu2(chpoxd)(H2O)(bpy)](NO3)·C2H5OH·H2O (1) and [Cu2(chmpoxd)-(H2O)(bpy)]Cl·3H2O (2), were synthesized and structurally characterized. The single-crystal X-ray diffraction analysis reveals that both the copper(II) ions in the two complexes are bridged by the cis-oxamido group, in which the exo-copper ions have square-pyramidal coordination geometries, while the inner ones are in a distorted square-pyramidal and a square-planar environment in complexes 1 and 2, respectively. The three dimensional supramolecular structures are constructed by hydrogen bonding and π–π stacking interactions. The reactivities towards DNA and protein BSA of the two complexes are studied both theoretically and experimentally. In vitro anticancer activities indicated that the two complexes are active against the selected tumor cell lines, and the anticancer activities are consistent with their DNA-binding affinities following the order 1 > 2.