The tumour suppressor p53 activates Puma-dependent apoptosis and p21-dependent cell-cycle arrest in response to DNA damage. Deletion of p21 improved stem-cell function and organ maintenance in progeroid mice with dysfunctional telomeres, but the function of Puma has not been investigated in this context. Here we show that deletion of Puma improves stem- and progenitor-cell function, organ maintenance and lifespan of telomere-dysfunctional mice. Puma deletion impairs the clearance of stem and progenitor cells that have accumulated DNA damage as a consequence of critically short telomeres. However, further accumulation of DNA damage in these rescued progenitor cells leads to increasing activation of p21. RNA interference experiments show that upregulation of p21 limits proliferation and evolution of chromosomal imbalances of Puma-deficient stem and progenitor cells with dysfunctional telomeres. These results provide experimental evidence that p53-dependent apoptosis and cell-cycle arrest act in cooperating checkpoints limiting tissue maintenance and evolution of chromosomal instability at stem- and progenitor-cell levels in response to telomere dysfunction. Selective inhibition of Puma-dependent apoptosis can result in temporary improvements in maintenance of telomere-dysfunctional organs.