Cohesin maintains genome integrity through its ability to bind and link DNA molecules via a Structural Maintenance of Chromatin (SMC) activity. These effects are manifested through its major function in sister chromatid cohesion, but also through activities during DNA replication, repair, and transcription. The array of cohesin functions can make interpreting cellular effects of cohesin loss difficult to interpret mechanistically. This is particularly important in cancer where cohesin subunit mutations are common, and where the identification of genetic dependencies would be useful for predicting the response of cohesin-mutated cells to genotoxic challenges. Here we performed a series of synthetic cytotoxicity screens with hypomorphic cohesin alleles in yeast to identify cellular pathways whose loss sensitizes cohesin-mutants to sublethal levels of genotoxic DNA damage. This dataset reveals important roles for cohesin in replication stress and homologous recombination regulation that can leave cohesin mutated cells with a dependency on translesion synthesis for survival.