Three new heteroscorpionate ligands, (2-hydroxyphenyl)bis(imidazol-1-yl)methane (HL1), (4-diethylamino-2-hydroxyphenyl)bis(imidazol-1-yl)methane (HL2) and (5-bromo-2-hydroxyphenyl)bis(imidazol-1-yl)methane (HL3), and their heteroleptic copper(II) complexes of the type [Cu(L1–3)diimine]ClO4 (1–6; where diimine =2,2′-bipyridyl or 1,10-phenanthroline) have been synthesized and characterized using spectroscopic methods. The molecular structure of ligand HL1 was determined by single-crystal X-ray diffraction. UV–visible, electron paramagnetic resonance and theoretical studies suggest a distorted square pyramidal geometry around copper(II) ion. Analyses of highest occupied and lowest unoccupied molecular orbitals have been used to explain the charge transfer taking place within the complexes. The antioxidant activities of the heteroscorpionate ligands and their heteroleptic copper(II) complexes were determined using ABTS, DPPH and H2O2 free radical scavenging assays with respect to standard antioxidant ascorbic acid. In molecular docking studies, the complexes showed π–π, hydrogen bonding, van der Waals and electrostatic interactions with fibroblast growth factor receptor kinase. In vitro cytotoxicity activities of ligands and copper(II) complexes were examined on human breast adenocarcinoma (MCF-7), cervical (HeLa) and lung (A549) cancer cell lines and normal human dermal fibroblast cell line using MTT assay. Complex 4 exhibited higher anticancer activity than the other complexes against all three cancer lines, being more potent than the standard drug cisplatin.