Mixed ligand copper(II) complexes containing derivatives of salicylic acid and heterocyclic ligands with nitrogen donor atoms have been the subject of various studies and reviews. In this paper, synthesis and characterization of the ternary copper(II) complexes of neocuproine (2,9-dimethyl-1,10-phenanthroline, Neo) and salicylate ligands (Sal) are reported. In addition, the crystal structures of ([Cu(H2O)(5-Cl-Sal)(Neo)] (1), [Cu(μ-Sal)(Neo)]2 (2), Cu2(μ-5-Cl-Sal)(5-Cl-HSal)2(Neo)2]·EtOH (3)) were determined. In order to compare structural and biological properties of the prepared complexes, spectroscopic and biological studies were performed. Results of X-ray diffraction show that prepared complexes form three types of crystal structures in a given system: monomeric, dimeric and dinuclear complex. The preliminary study on the DNA cleavage activity has shown that the complexes under study behave as the chemical nucleases in the presence of added hydrogen peroxide with slight differences in the activity (1 > 2 > 3). The complexes 1 and 2 exhibited nuclease activity itself indicating the interaction of complexes with the DNA. It has been proposed that the enhanced destructive effect of the complexes 1 and 2 on the DNA is a result of two possible mechanisms of action: (i) the conversion of closed circular DNA (form I) to the nicked DNA (form II) caused by the copper complex itself and (ii) damage of DNA by Reactive Oxygen Species (ROS)—products of the interaction of copper with hydrogen peroxide by means of Fenton reaction (hydroxyl radicals). Thus the biological activity of the prepared Cu(II) complexes containing derivatives of salicylic acid and phenanthroline molecules is substantiated by two independent mechanisms. While derivatives of salicylic acids in the coordination sphere of copper complexes are responsible for radical-scavenging activity (predominantly towards superoxide radical anion), the presence of chelating ligand 2,9-dimethyl-1,10-phenanthroline significantly enhances capability of Cu(II) complexes binding to DNA via intercalation.