Copper complexes [Cu(L1H)ClO4] (1) and [Cu(L2)NO3] (2), which are relevant to the metal site of the galactose oxidase enzyme, were synthesized and characterized by different spectroscopic methods. L1H2 and L2H2 [where L1H2 stands for 2,2'-((1E,1'E)(2,2'-(pyridine-2,6-diyl)bis(2-phenylhydrazin-2-yl-1-ylidene))bis(methanylylidene))diphenol and L2H2 stands for 6,6'-((1E,1'E)-(2,2'-(pyridine-2,6-diyl)bis(2-phenylhydrazin-2-yl-1-ylidene))bis(methanylylidene))bis(2,4-di-tert-butylphenol), H stands for dissociable proton] are pentadentate ligands. These ligands provide pyridyl N, two imine N, and two non-innocent phenoxyl and phenolato O donors, forming complex 1 as a non-radical complex, while complex 2 is a phenoxyl radical complex. The molecular structures of complexes 1 and 2 were authenticated by X-ray crystallography. Benzyl alcohol oxidation was investigated, and the conversion of 9,10-dihydroanthracene to anthracene was examined to scrutinize the H-atom abstraction reaction. Nuclease activity with complexes 1 and 2 was investigated by self-activated plasmid DNA (pBR322) cleavage. Non-innocent properties of the ligand-containing phenolato function were investigated by DFT calculations.