A few water soluble mixed ligand copper(ii) complexes of the type [Cu(bimda)(diimine)] 1-5, where bimda is N-benzyliminodiacetic acid and diimine is 2,2′-bipyridine (bpy, 1) or 1,10-phenanthroline (phen, 2) or 5,6-dimethyl-1,10-phenanthroline (5,6-dmp, 3) or 3,4,7,8-tetramethyl-1,10-phenanthroline (3,4,7,8-tmp, 4) and dipyrido[3,2-d: 2′,3′-f]quinoxaline (dpq, 5), have been successfully isolated and characterized by elemental analysis and other spectral techniques. The coordination geometry around copper(ii) in 2 is described as distorted square based pyramidal while that in 3 is described as square pyramidal. Absorption spectral titrations and competitive DNA binding studies reveal that the intrinsic DNA binding affinity of the complexes depends upon the diimine co-ligand, dpq (5) > 3,4,7,8-tmp (4) > 5,6-dmp (3) > phen (2) > bpy (1). The phen and dpq co-ligands are involved in the π-stacking interaction with DNA base pairs while the 3,4,7,8-tmp/5,6-dmp and bpy co-ligands are involved in respectively hydrophobic and surface mode of binding with DNA. The small enhancement in the relative viscosity of DNA upon binding to 1-5 supports the DNA binding modes proposed. Interestingly, 3 and 4 are selective in exhibiting a positive induced CD band (ICD) upon binding to DNA suggesting that they induce B to A conformational change. In contrast, 2 and 5 show CD responses which reveal their involvement in strong DNA binding. The complexes 2-4 are unique in displaying prominent double-strand DNA cleavage while 1 effects only single-strand DNA cleavage, and their ability to cleave DNA in the absence of an activator varies as 5 > 4 > 3 > 2 > 1. Also, all the complexes exhibit oxidative double-strand DNA cleavage activity in the presence of ascorbic acid, which varies as 5 > 4 > 3 > 2 > 1. The ability of the complexes to bind and cleave the protein BSA varies in the order 4 > 3 > 5 > 2 > 1. Interestingly, 3 and 4 cleave the protein non-specifically in the presence of H2O2 as an activator suggesting that they can act also as chemical proteases. It is remarkable that 2-5 exhibit cytotoxicity against human breast cancer cell lines (MCF-7) with potency higher than the widely used drug cisplatin indicating that they have the potential to act as effective anticancer drugs in a time dependent manner. The morphological assessment data obtained by using Hoechst 33258 staining reveal that 3 and 4 induce apoptosis much more effectively than other complexes. Also, the alkaline single-cell gel electrophoresis study (comet assay) suggests that the same complexes induce DNA fragmentation more efficiently than others. © The Royal Society of Chemistry 2015.