A key function of the cellular DNA damage response is to facilitate the bypass of replication fork-stalling DNA lesions. Template switch reactions allow such a bypass and involve the formation of DNA joint molecules (JMs) between sister chromatids. These JMs need to be resolved before cell division; however, the regulation of this process is only poorly understood. Here, we identify a regulatory mechanism in yeast that critically controls JM resolution by the Mus81–Mms4 endonuclease. Central to this regulation is a conserved complex comprising the scaffold proteins Dpb11 and Slx4 that is under stringent control. Cell cycle-dependent phosphorylation of Slx4 by Cdk1 promotes the Dpb11–Slx4 interaction, while in mitosis, phosphorylation of Mms4 by Polo-like kinase Cdc5 promotes the additional association of Mus81–Mms4 with the complex, thereby promoting JM resolution. Finally, the DNA damage checkpoint counteracts Mus81–Mms4 binding to the Dpb11–Slx4 complex. Thus, Dpb11–Slx4 integrates several cellular inputs and participates in the temporal program for activation of the JM-resolving nuclease Mus81.