Triple-negative breast cancer (TNBC) treatment offers only limited benefits, and it is very relevant given the significant number of deaths that it causes. DNA repair pathways can enable tumor cells to survive DNA damage that is induced by chemotherapeutic or radiation treatments. Histone deacetylase inhibitors (HDACi) inhibited DNA repair proteins. However, the detailed mechanisms for this inhibition remain unclear. In the present study, we investigated whether a newly developed HDACi, TMU-35435, could enhance etoposide cytotoxicity by inhibiting DNA repair proteins in triple-negative breast cancer. We found synergistic cytotoxicity following treatment of 4T1 cells with etoposide and TMU-35435. Furthermore, TMU-35435 enhances etoposide-induced DNA damage by inhibiting the DNA repair pathway (non-homologous end joining, NHEJ). TMU-35435 suppresses the NHEJ pathway through the ubiquitination of DNA-dependent protein kinase catalytic subunit (DNA-PKcs). In addition, TMU-35435 ubiquitinated DNA-PKcs by inducing the interaction between RNF144A (an E3 ligase) and DNA-PKcs. The combined treatment induced apoptosis and autophagic cell death in 4T1 cells. In an orthotopic breast cancer model, combined treatment with TMU-35435 and etoposide showed anti-tumor growth through the increase of DNA damage and cell death. Taken together, our data suggest that TMU-35435 enhances etoposide cytotoxicity by regulating ubiquitin-proteasome system and inhibiting the DNA repair pathway in TNBC.