Chromosome segregation begins when the cysteine protease, separase, cleaves the Scc1 subunit of cohesin at the metaphase-to-anaphase transition. Separase is inhibited prior to metaphase by the tightly bound securin protein, which contains a pseudosubstrate motif that blocks the separase active site. To investigate separase substrate specificity and regulation, here we develop a system for producing recombinant, securin-free human separase. Using this enzyme, we identify an LPE motif on the Scc1 substrate that is distinct from the cleavage site and is required for rapid and specific substrate cleavage. Securin also contains a conserved LPE motif, and we provide evidence that this sequence blocks separase engagement of the Scc1 LPE motif. Our results suggest that rapid cohesin cleavage by separase requires a substrate docking interaction outside the active site. This interaction is blocked by securin, providing a second mechanism by which securin inhibits cohesin cleavage.