In view of the rescue delay due to traffic congestion in the urban road network, this paper implemented real-time traffic control with congestion index constraints in emergency vehicle dispatching and proposed a two-stage optimization model and algorithm. In the first stage, salp swarm algorithm (SSA) was combined with Dijkstra algorithm, and a novel hybrid algorithm with new updating rules was designed to get the multiple alternative paths. In the second stage, an improved salp swarm algorithm (ISSA) with a population grouping strategy was proposed to obtain the best evacuation schemes and the optimal rescue paths of emergency vehicles. Results of the illustrative examples show that, after evacuation, the average travel time of all alternative paths is reduced by 24.22%, while traffic congestion indexes of the adjacent road sections almost unchanged. The computation time of the hybrid algorithm for obtaining the set number of alternative paths is 56.62% and 50.47% shorter than that of bat algorithm (BA) and SSA. For the solution of the evacuation model, the computation time of the ISSA is 33.51%, 30.15%, and 30.60% shorter than that of particle swarm optimization (PSO), BA, and SSA, and the optimal solution of the ISSA is 25.92%, 10.06%, and 0.97% better than that of PSO, BA, and SSA. That is, we shorten the emergency response time and control the adverse impact of traffic evacuation on background traffic. The improved algorithm has excellent performance. This study provides a new idea and method for emergency rescue of traffic accidents.