It is of clinical importance to identify biomarkers predicting the efficacy of DNA damaging drugs (genotoxins) so that nonresponders are not unduly exposed to the deleterious effects of otherwise inefficient drugs. Here, we initially focused on the bleomycin genotoxin because of the limited information about the genes implicated in the sensitivity or resistance to this compound. Using a whole-genome CRISPR/Cas9 gene knockout approach, we identified ASH2L, a core component of the H3K4 methyl transferase complex, as a protein required for bleomycin sensitivity in L1236 Hodgkin lymphoma. Knocking down ASH2L in these cells and in the NT2D1 testicular cancer cell line rendered them resistant to bleomycin, etoposide, and cisplatin but did not affect their sensitivity toward ATM or ATR inhibitors. ASH2L knockdown decreased cell proliferation and facilitated DNA repair via homologous recombination and nonhomologous end-joining mechanisms. Data from the Tumor Cancer Genome Atlas indicate that patients with testicular cancer carrying alterations in the ASH2L gene are more likely to relapse than patients with unaltered ASH2L genes. The cell models we have used are derived from cancers currently treated either partially (Hodgkin's lymphoma), or entirely (testicular cancer) with genotoxins. For such cancers, ASH2L levels could be used as a biomarker to predict the response to genotoxins. In situations where tumors are expressing low levels of ASH2L, which may allow them to resist genotoxic treatment, the use of ATR or ATM inhibitors may be more efficacious as our data indicate that ASH2L knockdown does not affect sensitivity to these inhibitors.