In this study, new azo-azomethine ligands L1H–L3H and their Cu(II) complexes were synthesized and characterized by the analytical and spectroscopic methods such as elemental analyses, infrared, mass, 1H and 13C NMR spectra. Molecular structures of the azo-azomethine ligands were determined by single crystal X-ray diffraction studies. X-ray data revealed that the compound L1H adopts azo-enamine tautomer form in the solid state while the compounds L2H and L3H favor azo-imine form. The harmonic oscillator model of aromaticity (HOMA) indexes for rings of synthesized azo-azomethine ligands were calculated in order to investigate of azo-enamine tautomer in the solid state. In L2H, the central phenol ring shows non-aromatic character with HOMA index value of 0.4872 suggesting the keto-amine tautomer in the solid state. All three azo-azomethine ligands involve in an intramolecular hydrogen bonding (N–H⋯O for L1H and O–H⋯N resulting in a S(6) graph set motif. The effect of solvents with different polarities on keto-enamine/phenol-imine tautomers was studied by UV-Vis spectroscopy. In the structure of the Cu(II) complexes, the central metal atom is coordinated to two phenolate oxygen atoms and two imine nitrogen atoms of two azo-azomethine molecules in a distorted square-planar geometry. All the synthesized azo-azomethine ligands and their Cu(II) complexes were screened for their cytotoxicity against HeLa (human uterus carcinoma) cell lines. Finally, antioxidant capacities of the compounds were determined by different antioxidant tests such as, free radical scavenging activity, metal chelating activity, and reduction power activity.