In this paper, we described the preparation, thorough characterization and evaluation of in vitro anticancer activity of copper(II) complexes containing various tripodal N-donor ligands, concretely [Cu(bpdmpz)Cl]ClO4 (1), [Cu(bdmpzp)Cl]ClO4 (2-ClO4), [Cu(bdmpzp)Cl]PF6 (2-PF6) and [Cu(tdmpza)Cl]ClO4 (3). The measurements of temperature-dependence of magnetic properties of 1–3 revealed weak antiferromagnetic exchange interactions. The complex [Cu(bedmpzp)Cl]PF6 (4) was the most cytotoxic one, with IC50 = 1.4 μM (A2780 cells), 8.3 μM (A2780R cells), 4.7 μM (HOS cells) and 10.8 μM (CaCo2 cells). The mass spectrometry-based interaction studies, involving selected sulfur-containing biomolecules and small model proteins, revealed pro-oxidant effects of complexes 1 and 4 and differences in stability of both complexes. Complex 1 formed an adduct, the formation of which was accompanied by the loss of one pendant arm, while the coordination of Cu(II) by tripodal ligand in 4 remained unchanged.