The novel mixed-ligand complexes derived from the parent antidepressant phenothiazine drug triflupromazine (TFP) were synthesized along with the secondary ligands glycine and histidine. [Cu(TFP)(Gly)Cl]·2H2O (1) and [Cu(TFP)(His)Cl]·2H2O (2) were examined for their in vitro biological properties. Cyclic voltammetry was used to study the binding of both complexes to CT-DNA. The two complexes were examined for antiviral, antiparasite, and anti-inflammatory applications. An in vitro cytotoxicity study on two different cancer cell lines, MCF-7, HepG2, and a normal cell line, HSF, shows promising selective cytotoxicity for cancer cells. An investigation of the cell cycle and apoptosis rates was evaluated by flow cytometry with Annexin V-FITC/Propidium Iodide (PI) staining of the treated cells. Gene expression and western blotting were carried out to determine the expression levels of the pro-apoptotic markers and the anti-apoptotic marker Bcl2. The tested complexes decreased cell viability and triggered apoptosis in human tumor cell lines. Molecular docking was also used to simulate Bcl2 inhibition. Finally, complex (2) has potent antitumor effects on human tumor cells, especially against HepG2 cells, as seen in the cellular drug uptake assay. Consequently, complex (2) may prove useful against cancer, especially liver cancer. For further understanding, it needs to be explored in vivo.