Human cancers frequently harbour mutations in DNA repair genes, rendering the use of DNA damaging agents as an effective therapeutic intervention. As therapy-resistant cells often arise, it is important to better understand the molecular pathways that drive resistance in order to facilitate the eventual targeting of such processes. We employ repair-defective diploid yeast as a model to demonstrate that, in response to genotoxic challenges, nearly all cells eventually undergo checkpoint adaptation, resulting in the generation of aneuploid cells with whole chromosome losses that have acquired resistance to the initial genotoxic challenge. We demonstrate that adaptation inhibition, either pharmacologically, or genetically, drastically reduces the occurrence of resistant cells. Additionally, the aneuploid phenotypes of the resistant cells can be specifically targeted to induce cytotoxicity. We provide evidence that TORC1 inhibition with rapamycin, in combination with DNA damaging agents, can prevent both checkpoint adaptation and the continued growth of aneuploid resistant cells.