Elucidation of mutagenic processes shaping cancer genomes is a fundamental problem whose solution promises insights into new treatment, diagnostic and prevention strategies1. Single-strand DNA–specific APOBEC cytidine deaminase(s) are major source(s) of mutation in several cancer types2,3,4. Previous indirect evidence implicated APOBEC3B as the more likely major mutator deaminase, whereas the role of APOBEC3A is not established5,6. Using yeast models enabling the controlled generation of long single-strand genomic DNA substrates7, we show that the mutation signatures of APOBEC3A and APOBEC3B are statistically distinguishable. We then apply three complementary approaches to identify cancer samples with mutation signatures resembling either APOBEC. Strikingly, APOBEC3A-like samples have over tenfold more APOBEC-signature mutations than APOBEC3B-like samples. We propose that APOBEC3A-mediated mutagenesis is much more frequent because APOBEC3A itself is highly proficient at generating DNA breaks8,9,10, whose repair can trigger the formation of single-strand hypermutation substrates.