RNA surveillance pathways detect and degrade defective transcripts to ensure RNA fidelity. We found that disrupted nuclear RNA surveillance is oncogenic. Cyclin-dependent kinase 13 (CDK13) is mutated in melanoma, and patient-mutated CDK13 accelerates zebrafish melanoma. CDK13 mutation causes aberrant RNA stabilization. CDK13 is required for ZC3H14 phosphorylation, which is necessary and sufficient to promote nuclear RNA degradation. Mutant CDK13 fails to activate nuclear RNA surveillance, causing aberrant protein-coding transcripts to be stabilized and translated. Forced aberrant RNA expression accelerates melanoma in zebrafish. We found recurrent mutations in genes encoding nuclear RNA surveillance components in many malignancies, establishing nuclear RNA surveillance as a tumor-suppressive pathway. Activating nuclear RNA surveillance is crucial to avoid accumulation of aberrant RNAs and their ensuing consequences in development and disease.