In the germline of animals, PIWI interacting (pi)RNAs protect the genome against the detrimental effects of transposon mobilization. In Drosophila, piRNA-mediated cleavage of transposon RNA triggers the production of responder piRNAs via ping-pong amplification. Responder piRNA 3' end formation by the nuclease Zucchini is coupled to the production of downstream trailer piRNAs, expanding the repertoire of transposon piRNA sequences. In Aedes aegypti mosquitoes, piRNAs are generated from viral RNA, yet, it is unknown how viral piRNA 3' ends are formed and whether viral RNA cleavage gives rise to trailer piRNA production. Here we report that in Ae. aegypti, virus- and transposon-derived piRNAs have sharp 3' ends, and are biased for downstream uridine residues, features reminiscent of Zucchini cleavage of precursor piRNAs in Drosophila. We designed a reporter system to study viral piRNA 3' end formation and found that targeting viral RNA by abundant endogenous piRNAs triggers the production of responder and trailer piRNAs. Using this reporter, we identified the Ae. aegypti orthologs of Zucchini and Nibbler, two nucleases involved in piRNA 3' end formation. Our results furthermore suggest that autonomous piRNA production from viral RNA can be triggered and expanded by an initial cleavage event guided by genome-encoded piRNAs.