We present a predict- correct trajectory propagation (PCTP) method for simulating nonequilibrium driven dynamics of the long-tiine bond-breaking event in an atomic force microscope (AFM). Whereas the parallel replica method can extend the time scale of molecular dynamics (MD) simulations of infrequent-event systems with high parallel efficiency, the second aspect of the time scale difficulty in MD simulations for slow-driven systems, namely, the unphysically high attempt frequency of an infrequent event, cannot be resolved by this method. Here, we take a gold nanojunction under mechanical pulling as a simulation system and demonstrate that the PCTP simulation is capable of capturing key transition dynamics of bond breaking predicted by accurate MD simulations in the activationless regime, such as at cryogenic temperature with high pulling rates. The PCTP algorithm includes three steps: (i) the trajectory prediction of the AFM tip, (ii) the atomic structural relaxation of the nanojunction, and (iii) the trajectory correction of the tip motion predicted by step (i). Application of the PCTP simulation to the bond breaking at AFM experimental pulling rates reveals different rupture mechanisms, depending on temperature and single -atom nanojunction structures, which are consistent with recent AFM bond-breaking observations.