Cas9 can cleave DNA in both blunt and staggered configurations, resulting in distinct editing outcomes, but what dictates the type of Cas9 incisions is largely unknown. In this study, we developed BreakTag, a versatile method for profiling Cas9-induced DNA double-strand breaks (DSBs) and identifying the determinants of Cas9 incisions. Overall, we assessed cleavage by SpCas9 at more than 150,000 endogenous on-target and off-target sites targeted by approximately 3,500 single guide RNAs. We found that approximately 35% of SpCas9 DSBs are staggered, and the type of incision is influenced by DNA:gRNA complementarity and the use of engineered Cas9 variants. A machine learning model shows that Cas9 incision is dependent on the protospacer sequence and that human genetic variation impacts the configuration of Cas9 cuts and the DSB repair outcome. Matched datasets of Cas9 and engineered variant incisions with repair outcomes show that Cas9-mediated staggered breaks are linked with precise, templated and predictable single-nucleotide insertions, demonstrating that a scission-based gRNA design can be used to correct clinically relevant pathogenic single-nucleotide deletions.