Centrosome amplification is a hallmark of human tumours. In flies, extra centrosomes cause spindle position defects that result in the expansion of the neural stem cell (NSC) pool and consequently in tumour formation. Here we investigated the consequences of centrosome amplification during mouse brain development and homeostasis. We show that centrosome amplification causes microcephaly due to inefficient clustering mechanisms, where NSCs divide in a multipolar fashion producing aneuploid cells that enter apoptosis. Importantly, we show that apoptosis inhibition causes the accumulation of highly aneuploid cells that lose their proliferative capacity and differentiate, thus depleting the pool of progenitors. Even if these conditions are not sufficient to halt brain development, they cause premature death due to tissue degeneration. Our results support an alternative concept to explain the etiology of microcephaly and show that centrosome amplification and aneuploidy can result in tissue degeneration rather than overproliferation and cancer.