Copper(II) complexes with an α-diimine show a wide variety of biological activities, such as antibacterial, antifungal, antioxidant and anticancer. In this work, we synthesized and structurally characterized two novel Cu(II) complexes with methyl 3-formyl-4-hydroxybenzoate (HL) and α-diimines: 2,2'-bipyridine (bipy) and 1,10-phenanthroline (phen). Crystal structure analysis shows that the formulas of the compounds are [Cu(bipy)(L)(BF4)] (1) and [Cu(phen)(L)(H2O)](BF4)·H2O (2), with BF4- as a ligand in complex 1, which is rarely coordinated to metals. Both complexes have a square pyramidal geometry, while DFT calculations showed that the most stable structures of complexes 1 and 2 in a water/DMSO mixture are square-planar derivatives [Cu(bipy)(L)]+ and [Cu(phen)(L)]+. The antibacterial activity of compounds was evaluated in vitro on four Gram-negative and four Gram-positive bacterial strains. Complex 2 showed greater antibacterial activity towards all bacterial strains comparable to the control compound Amikacin. Complex 2 exerted a strong cytotoxic effect against the tested cancer cell lines (IC50 values ranging from 0.32 to 0.44 μM). Both complexes caused apoptotic cell death in HeLa cells and a noticeable in vitro antiangiogenic effect. In the concentration range of 5 to 100 μM, the complexes showed the absence of a genotoxic effect and displayed a protective effect against oxidative DNA damage induced by H2O2 in human peripheral blood cells. The interaction between the compounds and calf-thymus DNA was evaluated by diverse techniques suggesting a tight binding, which was also confirmed by molecular docking. In addition, it was found that the complexes bind tightly and reversibly to bovine and human serum albumin.