To understand the design principles of the molecular interaction network associated with the irreversibility of cell apoptosis and the stability of cell surviving, we constructed a Boolean network integrating both the intrinsic and extrinsic pro-apoptotic pathways with pro-survival signal transduction pathways. We performed statistical analyses of the dependences of cell fate on initial states and on input signals. The analyses reproduced the well-known pro- and anti-apoptotic effects of key external signals and network components. We found that the external GF signal by itself did not change the apoptotic ratio from randomly chosen initial states when there is no external TNF signal, but can significantly offset apoptosis induced by the TNF signal. While a complete model produces the expected irreversibility of the apoptosis process, alternative models missing one or more of four selected inter-component connections indicate that the feedback loops directly involving the caspase 3 are essential for maintaining irreversibility of apoptosis. The feedback loops involving P53 showed compensating effects when those involving caspase 3 have been removed. The GF signal significantly increases the stability of the surviving states of the network. The apoptosis network seems to use different modules by design to control the irreversibility of the apoptosis process and the stability of the surviving states. Such a design may accommodate the needed plasticity for the network to adapt to different cellular environments: depending on the strength of external pro-surviving signals, apoptosis can be induced either easily or difficultly by pro-apoptotic signal of varying strengths, but proceed with invariable irreversibility.