A Cu(II) complex, that is, [Cu(CNC-B3)(IM-B7)](PF6)2, 1, containing CNC-B3 (L2) = CNC-pincer-vitamin B3 and IM-B7 (L3) = 1H-imidazole-1-methanamine-vitamin B7 conjugates, was developed as a potential chemotherapeutic agent for breast cancer cell lines. The Cu(II) complex brings about a remarkable in vitro cytotoxicity in comparison with cisplatin and tamoxifen against MDA-MB-231 and MCF-7 cancer cell lines. Interestingly, the Cu(II) complex was considerably less toxic to MRC-5 normal cells. The DNA/human serum albumin-binding capacity of the Cu(II) complex was confirmed by spectrometric methods and the molecular docking and ONIOM studies. The mechanistic pathway of DNA cleavage was studied by reactive oxygen species (ROS)-inhibiting agents. Furthermore, the Cu(II) complex affected the increasing level of the reactive oxygen species (ROS) and the decreasing level of glutathione in MCF-7 cells. The new complex induced major levels of MCF-7 cancer cell death by apoptosis.