Genome instability, including chromothripsis, is a hallmark of cancer. Cancer cells frequently contain micronuclei-small, nucleus-like structures formed by chromosome missegregation-that are susceptible to rupture, exposing chromatin to cytoplasmic nucleases. Through an unbiased, imaging-based small interfering RNA screen that targeted all 204 known and putative human nucleases, we identified a previously uncharacterized cytoplasmic endonuclease, NEDD4-binding protein 2 (N4BP2), that enters ruptured micronuclei and initiates DNA damage, leading to chromosome fragmentation. N4BP2 promoted genome rearrangements (including chromothripsis), formation of extrachromosomal DNA (ecDNA) in drug-induced gene amplification, tumorigenesis, and tumor cell proliferation in an induced model of human high-grade glioma. Analysis of more than 10,000 human cancer genomes revealed elevated N4BP2 expression to be predictive of chromothripsis and copy number amplifications, including ecDNA.