The post-translational modification of DNA damage response proteins with SUMO is an important mechanism to orchestrate a timely and orderly recruitment of repair factors to damage sites. After DNA replication stress and double-strand break formation, a number of repair factors are SUMOylated and interact with other SUMOylated factors, including the Yen1 nuclease. Yen1 plays a critical role in ensuring genome stability and unperturbed chromosome segregation by removing covalently linked DNA intermediates between sister chromatids that are formed by homologous recombination. Here we show how this important role of Yen1 depends on interactions mediated by non-covalent binding to SUMOylated partners. Mutations in the motifs that allow SUMO-mediated recruitment of Yen1 impair its ability to resolve DNA intermediates and result in chromosome mis-segregation and increased genome instability.