Genome integrity and cell survival are dependent on proper replication stress response. Multiple repair pathways addressing obstacles generated by replication stress arose during evolution, and a detailed understanding of these processes is crucial for treatment of numerous human diseases. Here, we investigated the strong negative genetic interaction between two proteases involved in the DNA replication stress response, yeast Wss1 and Ddi1. While Wss1 proteolytically acts on DNA-protein crosslinks, mammalian DDI1 and DDI2 proteins remove RTF2 from stalled forks via a proposed proteasome shuttle hypothesis. We show that the double-deleted Δddi1, Δwss1 yeast strain is hypersensitive to the replication drug hydroxyurea and that this phenotype can be complemented only by catalytically competent Ddi1 protease. Furthermore, our data show the key involvement of the helical domain preceding the Ddi1 protease domain in response to replication stress caused by hydroxyurea, offering the first suggestion of this domain's biological function. Overall, our study provides a basis for a novel dual protease-based mechanism enabling yeast cells to counteract DNA replication stress.