Fidelity of DNA replication is maintained using polymerase proofreading and the mismatch repair pathway. Tumors with loss of function of either mechanism have elevated mutation rates with characteristic mutational signatures. Here we report that tumors with concurrent loss of both polymerase proofreading and mismatch repair function have mutational patterns that are not a simple sum of the signatures of the individual alterations, but correspond to distinct, previously unexplained signatures: COSMIC database signatures 14 and 20. We then demonstrate that in all five cases in which the chronological order of events could be determined, polymerase epsilon proofreading alterations precede the defect in mismatch repair. Overall, we illustrate that multiple distinct mutational signatures can result from different combinations of a smaller number of mutational processes (of either damage or repair), which can influence the interpretation and discovery of mutational signatures.