In mitosis, the spindle assembly checkpoint (SAC) ensures genome stability by delaying chromosome segregation until all sister chromatids have achieved bipolar attachment to the mitotic spindle. The SAC is imposed by the mitotic checkpoint complex (MCC), whose assembly is catalysed by unattached chromosomes and which binds and inhibits the anaphase-promoting complex/cyclosome (APC/C), the E3 ubiquitin ligase that initiates chromosome segregation. Here, using the crystal structure of Schizosaccharomyces pombe MCC (a complex of mitotic spindle assembly checkpoint proteins Mad2, Mad3 and APC/C co-activator protein Cdc20), we reveal the molecular basis of MCC-mediated APC/C inhibition and the regulation of MCC assembly. The MCC inhibits the APC/C by obstructing degron recognition sites on Cdc20 (the substrate recruitment subunit of the APC/C) and displacing Cdc20 to disrupt formation of a bipartite D-box receptor with the APC/C subunit Apc10. Mad2, in the closed conformation (C-Mad2), stabilizes the complex by optimally positioning the Mad3 KEN-box degron to bind Cdc20. Mad3 and p31^comet (also known as MAD2L1-binding protein) compete for the same C-Mad2 interface, which explains how p31^comet disrupts MCC assembly to antagonize the SAC. This study shows how APC/C inhibition is coupled to degron recognition by co-activators.