Copper compounds can be alternatives to platinum-based anticancer drugs. This study investigated the effects of a series of ternary copper(II) complexes, [Cu(phen)(aa)(H2O)]NO3·xH2O 1-4 (phen = 1,10-phenanthroline; aa = gly (1), DL-ala (2), sar (3), C-dmg (4)), on metastatic and cisplatin-resistant MDA-MB-231 breast cancer cells and MCF10A non-cancerous breast cells, and some aspects of the mechanisms. These complexes were distinctively more antiproliferative towards and induced greater apoptotic cell death in MDA-MB-231 than in MCF10A cells. 2 and 4 could induce cell cycle arrest only in cancer cells. Further evidence from DCFH-DA assay showed higher induction of reactive oxygen species (ROS) in treated cancer cells but minimal ROS increase in normal cells. DNA double-strand breaks, via a γ-H2AX assay, were only detected in cancer cells treated with 5 μM of the complexes. These complexes poorly inhibited chymotrypsin-like activity in the 20S rabbit proteasome while they did not inhibit the three proteolytic sites of MDA-MB-231 cells at 10 μM. However, the complexes could inhibit degradation of ubiquinated proteins of MDA-MB-231 cells. In addition, compound 4 was found to be effective against cervical (Hela), ovarian (SKOV3), lung (A549, PC9), NPC (Hone1, HK1, C666-1), breast (MCF7, T47D), lymphoma and leukemia (Nalmawa, HL60) and colorectal (SW480, SW48, HCT118) cancer cell lines with IC50 values (24 h) in the 1.7-19.0 μM range. Single dose NCI60 screening of 4 showed the complex to be highly cytotoxic to most cancer cell types and more effective than cisplatin.