The Artemis nuclease and tyrosyl-DNA phosphodiesterase (TDP1) are each capable of resolving protruding 3-phosphoglycolate (PG) termini of DNA double-strand breaks (DSBs). Consequently, both a knockout of Artemis and a knockout/knockdown of TDP1 rendered cells sensitive to the radiomimetic agent neocarzinostatin (NCS), which induces 3-PG-terminated DSBs. Unexpectedly, however, a knockdown or knockout of TDP1 in Artemis-null cells did not confer any greater sensitivity than either deficiency alone, indicating a strict epistasis between TDP1 and Artemis. Moreover, a deficiency in Artemis, but not TDP1, resulted in a fraction of unrepaired DSBs, which were assessed as 53BP1 foci. Conversely, a deficiency in TDP1, but not Artemis, resulted in a dramatic increase in dicentric chromosomes following NCS treatment. An inhibitor of DNA-dependent protein kinase, a key regulator of the classical nonhomologous end joining (C-NHEJ) pathway sensitized cells to NCS, but eliminated the sensitizing effects of both TDP1 and Artemis deficiencies. These results suggest that TDP1 and Artemis perform different functions in the repair of terminally blocked DSBs by the C-NHEJ pathway, and that whereas an Artemis deficiency prevents end joining of some DSBs, a TDP1 deficiency tends to promote DSB misjoining.