During mitosis, the genome is transformed from a decondensed, transcriptionally active state to a highly condensed, transcriptionally inactive state. Mitotic chromosome reorganization is marked by the general attenuation of transcription on chromosome arms, yet how the cell regulates nuclear and chromatin-associated RNAs after chromosome condensation and nuclear envelope breakdown is unknown. SAF-A/hnRNPU is an abundant nuclear protein with RNA-to-DNA tethering activity, coordinated by two spatially distinct nucleic acid–binding domains. Here we show that RNA is evicted from prophase chromosomes through Aurora-B–dependent phosphorylation of the SAF-A DNA-binding domain; failure to execute this pathway leads to accumulation of SAF-A–RNA complexes on mitotic chromosomes, defects in metaphase chromosome alignment, and elevated rates of chromosome missegregation in anaphase. This work reveals a role for Aurora-B in removing chromatin-associated RNAs during prophase and demonstrates that Aurora-B–dependent relocalization of SAF-A during cell division contributes to the fidelity of chromosome segregation.