Precise regulation of centrosome number is critical for accurate chromosome segregation and the maintenance of genomic integrity. In nontransformed cells, centrosome loss triggers a p53-dependent surveillance pathway that protects against genome instability by blocking cell growth. However, the mechanism by which p53 is activated in response to centrosome loss remains unknown. Here, we have used genome-wide CRISPR/Cas9 knockout screens to identify a USP28-53BP1-p53-p21 signaling axis at the core of the centrosome surveillance pathway. We show that USP28 and 53BP1 act to stabilize p53 after centrosome loss and demonstrate this function to be independent of their previously characterized role in the DNA damage response. Surprisingly, the USP28-53BP1-p53-p21 signaling pathway is also required to arrest cell growth after a prolonged prometaphase. We therefore propose that centrosome loss or a prolonged mitosis activate a common signaling pathway that acts to prevent the growth of cells that have an increased propensity for mitotic errors.