This research was aimed at finding the cytotoxic potential of the mixed ligand copper(II) complex [Cu(tdp)(phen)](ClO4)—where H(tdp) is the tetradentate ligand 2-[(2-(2-hydroxyethylamino)-ethylimino)methyl]phenol, and phen is 1,10-phenanthroline—to two genotypically different breast cancer cells, MCF-7 (p53+ and ER+) and MDA-MB-231 (p53- and ER-). The complex has been already shown to be cytotoxic to ME180 cervical carcinoma cells. The special focus in this study was the induction of cell death by apoptosis and necrosis, and its link with ROS. The treatment brought about nuclear fragmentation, phosphatidylserine externalization, disruption of mitochondrial trans-membrane potential, DNA damage, cell cycle arrest at sub-G1 phase, and increase of ROS generation, followed by apoptotic death of cells during early hours and a late onset of necrosis in the cells surviving the apoptosis. The efficacy of the complex against genotypically different breast cancer cells is attributed to a strong association through p53-mitochondrial redox—cell cycle junction. The ADMET properties and docking of the complex at the active site of Top1 are desirable attributes of a lead molecule for development into a therapeutic. Thus, it is shown that the copper(II)–phenolate complex[Cu(tdp)(phen)]+ offers potential to be developed into a therapeutic for breast cancers in general and ER-negative ones in particular.