A series of thiosemicarbazone-coumarin hybrids (HL1-HL3 and H2L4) has been synthesised in 12 steps and used for the preparation of mono- and dinuclear copper(II) complexes, namely Cu(HL1)Cl2 (1), Cu(HL2)Cl2 (2), Cu(HL3)Cl2 (3) and Cu2(H2L4)Cl4 (4), isolated in hydrated or solvated forms. Both the organic hybrids and their copper(II) and dicopper(II) complexes were comprehensively characterised by analytical and spectroscopic techniques, i.e., elemental analysis, ESI mass spectrometry, 1D and 2D NMR, IR and UV–vis spectroscopies, cyclic voltammetry (CV) and spectroelectrochemistry (SEC). Re-crystallisation of 1 from methanol afforded single crystals of copper(II) complex with monoanionic ligand Cu(L1)Cl, which could be studied by single crystal X-ray diffraction (SC-XRD). The prepared copper(II) complexes and their metal-free ligands revealed antiproliferative activity against highly resistant cancer cell lines, including triple negative breast cancer cells MDA-MB-231, sensitive COLO-205 and multidrug resistant COLO-320 colorectal adenocarcinoma cell lines, as well as in healthy human lung fibroblasts MRC-5 and compared to those for triapine and doxorubicin. In addition, their ability to reduce the tyrosyl radical in mouse R2 protein of ribonucleotide reductase has been ascertained by EPR spectroscopy and the results were compared with those for triapine.