Five innovative ternary copper(II) complexes [Cu(OH-PIP)(Phe)Cl](1), [Cu(OH-PIP)(Gly)(H2O)]NO3·2H2O (2), [Cu(OH-PIP)(Ala)(Cl)]·H2O (3), [Cu(OH-PIP)(Met)]PF6·2H2O (4), and [Cu(OH-PIP)(Gln)(H2O)](Cl)·3H2O (5) have been synthesized and characterized by infrared spectroscopy, elemental analysis, and single crystal X-ray diffraction analysis. X-ray crystallography indicates that all Cu atoms are five-coordinated in a square-pyramidal configuration. The complexes have been screened for cytotoxicity against human breast cancer cell lines MCF-7, MDA-MB-231, and CAL-51. The best anticancer activity is obtained with triple-negative breast cancer CAL-51 and MDA-MB-231 cell lines, with IC50 values in the range of 0.082-0.69 μM. Importantly, the copper compounds were more effective than carboplatin at triggering cell death. Mechanistically, the complexes inhibit proteasomal chymotrypsin-like activity, and docking studies reveal their 20S proteasome binding sites. As a consequence, they cause the accumulation of ubiquitinated proteins, inhibit cell proliferation, and induce apoptosis. In addition, these copper complexes decrease the stemness of triple-negative breast cancer cells and have synergistic effects with CBP on TNBC cells, indicating their great potential as a novel therapy for triple-negative breast cancer.