The genome engineering capability of the CRISPR/Cas system depends on the DNA repair machinery to generate the final outcome. Several genes can have an impact on mutations created, but their exact function and contribution to the result of the repair are not completely characterised. This lack of knowledge has limited the ability to comprehend and regulate the editing outcomes. Here, we measure how the absence of 21 repair genes changes the mutation outcomes of Cas9-generated cuts at 2,812 synthetic target sequences in mouse embryonic stem cells. Absence of key non-homologous end joining genes Lig4, Xrcc4, and Xlf abolished small insertions and deletions, while disabling key microhomology-mediated repair genes Nbn and Polq reduced frequency of longer deletions. Complex alleles of combined insertion and deletions were preferentially generated in the absence of Xrcc6. We further discover finer structure in the outcome frequency changes for single nucleotide insertions and deletions between large microhomologies that are differentially modulated by the knockouts. We use the knowledge of the reproducible variation across repair milieus to build predictive models of Cas9 editing results that outperform the current standards. This work improves our understanding of DNA repair gene function, and provides avenues for more precise modulation of CRISPR/Cas9-generated mutations.