Mitotic spindles are critical for accurate chromosome segregation. Centrosomes, the primary microtubule nucleating centers of animal cells, play key roles in forming and orienting mitotic spindles. However, the survival of Drosophila without centrosomes suggested they are dispensable in somatic cells, challenging the canonical view. We used fly wing disc epithelia as a model to resolve these conflicting hypotheses, revealing that centrosomes play vital roles in spindle assembly, function, and orientation. Many acentrosomal cells exhibit prolonged spindle assembly, chromosome missegregation, DNA damage, misoriented divisions, and eventual apoptosis. We found that multiple mechanisms buffer the effects of centrosome loss, including alternative microtubule nucleation pathways and the spindle assembly checkpoint. Apoptosis of acentrosomal cells is mediated by JNK signaling, which also drives compensatory proliferation to maintain tissue integrity and viability. These data reveal the importance of centrosomes in fly epithelia and demonstrate the robust compensatory mechanisms at the cellular and organismal level.