Developing pharmacological strategies for controlling ionizing radiation (IR)-induced cell death is important for both mitigating radiation damage and alleviating the side effects of anti-cancer radiotherapy manifested in surrounding tissue morbidity. Exposure to IR often triggers the onset of p53-dependent apoptotic pathways. Here we build a stochastic model of p53 induced apoptosis comprised of coupled modules of nuclear p53 activation, mitochondrial cytochrome c release and cytosolic caspase activation that also takes into account cellular heterogeneity. Our simulations show that the strength of p53 transcriptional activity and its coupling (or timing with respect) to mitochondrial pore opening are major determinants of cell fate: for systems where apoptosis is elicited via a p53-transcription-independent mechanism, direct activation of Bax by p53 becomes critical to IR-induced-damage initiation. We further show that immediate administration of PUMA inhibitors following IR exposure effectively suppresses excessive cell death, provided that there is a strong caspase/Bid feedback loop; however, the efficacy of the treatment diminishes with increasing delay in treatment implementation. In contrast, the combined inhibition of Bid and Bax elicits an anti-apoptotic response that is effective over a range of time delays.