The development of active therapeutic agents to treat highly metastatic cancer while minimizing damage to healthy cells is of utmost importance. Due to potential antioxidant properties, hydroxycinnamic acid derivatives (caffeic acid and p-coumaric acids) were found to inhibit highly metastatic breast cancer cell growth both in vitro and in vivo without much effect on normal cells. Especially due to the structure-activity relationships, ester and amide derivatives of hydroxycinnamic acids are reported to gain much higher radical scavenging ability than their naked hydroxycinnamic acid analogs like caffeic acid and p-coumaric acid. These results prompted us to design a set of ligands by incorporating an amide moiety on caffeic acid and p-coumaric acid to achieve the least toxicity towards healthy cell lines. Further, the Cu(II) complexes of amide-coupled caffeic acid and p-coumaric acid ligands have been explored for their therapeutic activity on triple-negative breast cancer and other cancer cells like colon, and prostate cancer. The Cu(II) complexes (4 & 5) were characterized by UV-Vis spectroscopy, FTIR, and X-band EPR spectroscopy. The trigonal bipyramidal geometry of complexes was confirmed by the X-band EPR spectra recorded in solution state at liquid N2 temperature. The purity of the complexes was determined by elemental analysis and HPLC traces. Initially, Calf thymus DNA (ct-DNA) binding studies with the complexes were explored. The results suggested the complexes (4 & 5) bind majorly through an intercalative mode of binding with ct-DNA, whereas no significant binding was observed for the bare organic ligands (2 & 3). The intercalation binding modes of 4 and 5 were further supported by UV-visible spectroscopy, ct-DNA melting point analysis, and CD spectroscopy. Moreover, these complexes showed better activity towards cisplatin-resistant TNBC cell lines (4T1, a TNBC cell line derived from the mammary gland tissue of a mouse). The combination of antioxidants and Cu(II) as the metal center made the complexes more cytotoxic toward cancer cell lines (4T1) (IC50 ∼ 3.5 ± 2.5 μM) and the least toxic toward healthy cells (L929) (IC50 ∼ 15 ± 5 μM). Finally, the mechanism of cell death was studied using JC-1 staining and a cell colony formation assay. These studies might help in designing safer anticancer drugs for treating more aggressive types of cancer.