The Saccharomyces cerevisiae Rad1/Rad10 complex is a multifunctional, structure-specific endonuclease that processes UV-induced DNA lesions, recombination intermediates, and inter-strand DNA crosslinks. However, we do not know how Rad1/Rad10 recognizes these structurally distinct target molecules or how it is incorporated into the protein complexes capable of incising divergent substrates. Here, we have determined the order and hierarchy of assembly of the Rad1/Rad10 complex, Saw1, Slx4, and Msh2/Msh3 complex at a 3' tailed recombination intermediate. We found that Saw1 is a structure-specific DNA binding protein with high affinity for splayed arm and 3'-flap DNAs. By physical interaction, Saw1 facilitates targeting of Rad1 at 3' tailed substrates in vivo and in vitro, and enhances 3' tail cleavage by Rad1/Rad10 in a purified system in vitro. Our results allow us to formulate a model of Rad1/Rad10/Saw1 nuclease complex assembly and 3' tail removal in recombination.