The reaction of the ditopic bis(benzoylhydrazone) of isophthalaldehyde (H2L) with copper(II) acetate in methanol under aerobic conditions afforded a green solid that contains the tetranuclear complex [Cu4L*2(OCH3)2] (1). The ligand L*, a bis(benzoylhydrazone) of 2,6‐diformylphenol, resulted from hydroxylation of the corresponding isophthalaldehyde derivative. H2L and 1 were characterized by different spectroscopic techniques, and their molecular structures were confirmed by single‐crystal X‐ray diffraction. The reaction of H2L with copper(II) under argon, on the other hand, resulted in a brown diamagnetic solid [Cu2L]·H2O (2) containing copper(I), which was readily transformed into 1 when exposed to air. In contrast, the reaction with [Cu(CH3CN)4][BF4] afforded a mononuclear complex [Cu(H2L)][BF4]·H2O (3), and single crystals of [Cu(H2L)2][BF4] (4) were isolated from its dichloromethane solution. H2L cleaved plasmid DNA in the presence of copper(II) independently of any reducing agent, but more efficiently when ascorbate was present. The cleavage process is likely oxidative because the enzyme catalase, which decomposes hydrogen peroxide, quenched the reaction. In the absence of ascorbate, the ligand H2L presumably acts as the reductant in the redox reaction, as exploited also in the synthesis of 1. As a consequence, a variety of reactive oxygen species were generated, eventually also leading to the cleavage of DNA (“self‐activating” chemical nuclease).