Polynuclear platinum(II) complexes represent a class of great prospective Pt-based antitumor drugs that may expand the antitumor spectrum and overcome the clinical problems of drug resistance and side effects of platinum-based drugs. Herein, a novel star-shaped trinuclear platinum(II) complex [Pt3(L-3H)Cl3] (1, L = 2,4,6-tris[(2-hydroxybenzyl)(2-pyridylmethyl)amine]-1,3,5-triazine) and its monomer [Pt(L'-H)Cl] (2, L' = (2-hydroxybenzyl)(2-pyridylmethyl)amine) were synthesized and characterized. The in vitro antiproliferative activities of complexes 1 and 2 against a panel of human cancer cell lines including MDA-MB-231 (triple-negative breast cancer, TNBC), MCF-7 (breast), HepG-2 (liver), and A549 (lung) were investigated. The results revealed that 1 exhibited much higher antiproliferative properties than its monomer 2 against the tested cell lines. Importantly, 1 possessed 3.3-fold higher antiproliferative activity as compared with cisplatin against the TNBC cell line MDA-MB-231. Another TNBC cell line MDA-MB-468 is also sensitive to 1. The results indicated that 1 might have the potential to act as a candidate for the treatment of TNBC. Cellular uptake and distribution studies showed that 1 could pass through the membrane of cells and enter into cells and mainly accumulate in the nuclei and mitochondria. 1 could bind to DNA in a cooperative groove-electrostatic-platinating binding mode and induce stronger DNA double-strand breaks (DSBs) and damaging effects on MDA-MB-231 than cisplatin (upregulation of γ-H2AX). Moreover, the DNA damage could not be easily repaired (upregulation of p53), which would exert a much positive influence on the overcoming of drug resistance. Additionally, flow cytometry studies showed that 1 arrested the cell cycle in the G0/G1 phase, induced mitochondrial membrane depolarization, increased ROS generation, and induced cell apoptosis. The results demonstrated that 1 could target simultaneously mitochondria and nuclei that gave rise to mitochondrial injury and DNA damage and ultimately efficiently promote the apoptotic death of tumor cells. Further mechanistic studies showed that 1 induced MDA-MB-231 cell apoptosis via the p53-mediated mitochondrial pathway by upregulating Bax and cytochrome c and downregulating Bcl-2 proteins, leading to the activation of caspase-3 and upregulation of the cleaved-PARP level. Taken together, 1 with such a synergic mechanism has great potential to be an effective anticancer agent that can overcome treatment resistance in TNBC.