The multisubunit ubiquitin ligase APC/C (anaphase-promoting complex/cyclosome) is essential for mitosis by promoting timely degradation of cyclin B1. APC/C is tightly regulated by the spindle assembly checkpoint (SAC), which involves MPS1 and MAD2-dependent temporal inhibition of APC/C. We analyzed the contribution of the APC/C subunits APC7 and APC16 to APC/C composition and function in human cells. APC16 is required for APC7 assembly into APC/C, whereas APC16 assembles independently of APC7. APC7 and APC16 knockout cells display no major defects in mitotic progression, cyclin B1 degradation, or SAC response, but APC/C lacking these two subunits shows reduced ubiquitylation activity in vitro. Strikingly, deletion of APC7 or APC16 is sufficient to provide synthetic viability to MAD2 deletion. ΔAPC7ΔMAD2 cells display accelerated mitosis and require SAC-independent MPS1 function for genome stability. These findings reveal that the composition of APC/C critically influences the importance of the SAC in humans. Anaphase-promoting complex/cyclosome (APC/C) is an essential regulator of mitosis in eukaryotes. Wild et al. show that the APC/C subunits APC7 and APC16 are not required for mitosis in normal cells. However, genetic deletion of these subunits provides synthetic viability to cells lacking the spindle assembly checkpoint.