Human development relies on the correct replication, maintenance and segregation of our genetic blueprints. How these processes are monitored across embryonic lineages, and why genomic mosaicism varies during development remain unknown. Using pluripotent stem cells, we identify that several patterning signals-including WNT, BMP, and FGF-converge into the modulation of DNA replication stress and damage during S-phase, which in turn controls chromosome segregation fidelity in mitosis. We show that the WNT and BMP signals protect from excessive origin firing, DNA damage and chromosome missegregation derived from stalled forks in pluripotency. Cell signalling control of chromosome segregation declines during lineage specification into the three germ layers, but re-emerges in neural progenitors. In particular, we find that the neurogenic factor FGF2 induces DNA replication stress-mediated chromosome missegregation during the onset of neurogenesis, which could provide a rationale for the elevated chromosomal mosaicism of the developing brain. Our results highlight roles for morphogens and cellular identity in genome maintenance that contribute to somatic mosaicism during mammalian development.