In pluripotent stem cells, DNA damage triggers loss of pluripotency and apoptosis as a safeguard to exclude damaged DNA from the lineage. An intricate DNA damage response (DDR) signaling network ensures that the response is proportional to the severity of the damage. We combined an RNA interference screen targeting all kinases, phosphatases, and transcription factors with global transcriptomics and phosphoproteomics to map the DDR in mouse embryonic stem cells treated with the DNA cross-linker cisplatin. Networks derived from canonical pathways shared in all three data sets were implicated in DNA damage repair, cell cycle and survival, and differentiation. Experimental probing of these networks identified a mode of DNA damage-induced Wnt signaling that limited apoptosis. Silencing or deleting the p53 gene demonstrated that genotoxic stress elicited Wnt signaling in a p53-independent manner. Instead, this response occurred through reduced abundance of Csnk1a1 (CK1α), a kinase that inhibits β-catenin. Together, our findings reveal a balance between p53-mediated elimination of stem cells (through loss of pluripotency and apoptosis) and Wnt signaling that attenuates this response to tune the outcome of the DDR.