Traffic accident management as an approach to improve public security and reduce economic losses has received public attention for a long time, among which traffic accidents post-impact prediction (TAPIP) is one of the most important procedures. However, existing systems and methodologies for TAPIP are insufficient for addressing the problem. The drawbacks include ignoring the recovery process after clearance and failing to make comprehensive prediction in both time and space domain. To this end, we build a 3-stage TAPIP model on highways, using the technology of spiking neural networks (SNNs) and convolutional neural networks (CNNs). By dividing the accident lifetime into two phases, i.e., clean-up phase and recovery phase, the model extracts characteristics in each phase and achieves prediction of spatial-temporal post-impact variables (e.g., clean-up time, recovery time, and accumulative queue length). The framework takes advantage of SNNs to efficiently capture accident spatial-temporal features and CNNs to precisely represent the traffic environment. Integrated with an adaptation and updating mechanism, the whole system works autonomously in an online manner that continues to self-improve during usage. By testing with a new dataset CASTA pertaining to California statewide traffic accidents on highways collected in four years, we prove that the proposed model achieves higher prediction accuracy than other methods (e.g., KNN, shockwave theory, and ANNs). This work is the introduction of SNNs in the traffic accident prediction domain and also a complete description of post-impact in the whole accident lifetime.