Syntheses and crystal structures of four new hydrazone-based Cu(II) complexes, [{Cu(L1)(H2O)}2(μ-pyraz)](ClO4)2 (1), [{Cu(L1)(OClO3)}2(μ-4,4′-bipy)] (2), [{Cu(L2H)}(μ-pyraz){Cu(L2H)(OClO3)}].(ClO4) (3) and [{Cu(L2)}2(μ-bpe)] (4) [L1H = condensation product of benzhydrazide and pyridine-2-carbaldehyde and L2H2 = condensation product of benzoyl acetone and benzhydrazide], bridged by various organic spacers [pyrazine (pyraz), 4,4′-bipyridine (4,4′-bipy) and 1,2-di(4-pyridyl)ethane (bpe)] are reported in this paper. The single-crystal X-ray crystallographic studies reveal that all are dinuclear units where 1 and 3 form strong intermolecular H-bonding to form sheets of interconnected ions, whereas 2 forms sheets of dinuclear chains through π–π interactions; in 4, molecules are linked only through van der Waals interactions. The variable-temperature magnetic moment studies reveal that 1 and 3 show antiferromagnetic coupling between the Cu(II) centers at lower temperatures. The binding ability of 1 with calf thymus DNA [CT-DNA] is reported using various spectroscopic studies (UV-Vis titration, circular dichroism and fluorescence). The binding constants of 1 with CT-DNA, as calculated by different methodologies, are of the order of 105 M−1. The mode of interaction between 1 and CT-DNA has been predicted using circular dichroic (CD) spectroscopy, where it has been shown that 1 most probably interacts with DNA via intercalation between the base pairs leading to a change in B-DNA conformation. 1 is also able to cleave supercoiled (SC) plasmid DNA pUC19 in a time and dose dependent manner as demonstrated by agarose gel electrophoresis, and also demonstrates its potential to cleave the SC plasmid DNA via both oxidative and hydrolytic mechanisms. Approximately 50% of leukemic cells are found to be dead when two representative leukemic cell lines are exposed to 1 (∼80 μM) even for 24 h as determined by different cell cytotoxicity assays. Preliminary results also showed that, at 20 μM, 1 could selectively induce apoptosis in leukemic cells without affecting normal lymphocytes.