Cell extrusion is a mechanism of cell elimination that is used by organisms as diverse as sponges, nematodes, insects and mammals1-3. During extrusion, a cell detaches from a layer of surrounding cells while maintaining the continuity of that layer4. Vertebrate epithelial tissues primarily eliminate cells by extrusion, and the dysregulation of cell extrusion has been linked to epithelial diseases, including cancer1,5. The mechanisms that drive cell extrusion remain incompletely understood. Here, to analyse cell extrusion by Caenorhabditis elegans embryos3, we conducted a genome-wide RNA interference screen, identified multiple cell-cycle genes with S-phase-specific function, and performed live-imaging experiments to establish how those genes control extrusion. Extruding cells experience replication stress during S phase and activate a replication-stress response via homologues of ATR and CHK1. Preventing S-phase entry, inhibiting the replication-stress response, or allowing completion of the cell cycle blocked cell extrusion. Hydroxyurea-induced replication stress6,7 triggered ATR-CHK1- and p53-dependent cell extrusion from a mammalian epithelial monolayer. We conclude that cell extrusion induced by replication stress is conserved among animals and propose that this extrusion process is a primordial mechanism of cell elimination with a tumour-suppressive function in mammals.