Five-coordinate Cu(II) complexes, [Cu(Ln)X]ClO4/PF6, where Ln = piperazine ligands bearing two pyridyl arms and X = ClO4− for Ln = L1 (1-ClO4), L2 (2-ClO4), L3 (3-ClO4), and L6 (6-ClO4) as well as [Cu(Ln)Cl]PF6 for Ln = L1 (1-Cl), L4 (4-Cl), and L5 (5-Cl) have been synthesized and characterized by spectroscopic techniques. The molecular structures of the last two complexes were determined by X-ray crystallography. In aqueous acetonitrile solutions, molar conductivity measurements and UV-VIS spectrophotometric titrations of the complexes revealed the hydrolysis of the complexes to [Cu(Ln)(H2O)]2+ species. The biological activity of the Cu(II) complexes with respect to DNA cleavage and cytotoxicity was investigated. At micromolar concentration within 2 h and pH 7.4, DNA cleavage rate decreased in the order: 1-Cl ≈ 1-ClO4 > 3-ClO4 ≥ 2-ClO4 with cleavage enhancements of up to 23 million. Complexes 4-Cl, 5-Cl, and 6-ClO4 were inactive. In order to elucidate the cleavage mechanism, the cleavage of bis(4-nitrophenyl)phosphate (BNPP) and reactive oxygen species (ROS) quenching studies were conducted. The mechanistic pathway of DNA cleavage depends on the ligand’s skeleton: while an oxidative pathway was preferable for 1-Cl/1-ClO4, DNA cleavage by 2-ClO4 and 3-ClO4 predominantly proceeds via a hydrolytic mechanism. Complexes 1-ClO4, 3-ClO4, and 5-Cl were found to be cytotoxic against A2780 cells (IC50 30–40 µM). In fibroblasts, the IC50 value was much higher for 3-ClO4 with no toxic effect.