Interacts with eme1 to form a DNA structure-specific endonuclease with substrate preference for branched DNA structures with a 5'-end at the branch nick. Typical substrates include 3'-flap structures, D-loops, replication forks and nicked Holliday junctions. May be required in mitosis for the processing of stalled or collapsed replication fork intermediates. May be required in meiosis for the repair of meiosis-specific double strand breaks subsequent to single-end invasion (SEI). Interacts with eme1. Associates with chromatin. Interacts with the FHA domain of cds1, and this may require prior phosphorylation of Thr-275. Phosphorylated in a cds1-dependent manner in response to hydroxyurea (HU) treatment. This phosphorylation promotes dissociation of mus81 from chromatin which may prevent cleavage of intact stalled replication forks. S.pombe appears to be critically dependent on the mus81-eme1 endonuclease for the resolution of meiotic crossovers. This may be due to the absence of an alternate pathway for crossover resolution such as the MSH4-MSH5 pathway which exists in S.cerevisiae and other eukaryotes. Belongs to the XPF family.