Medical assistance is crucial to disaster management. In particular, the situation of survivors as well as the environmental information after disasters should be collected and sent back to cloud/data centers immediately for further interpretation and analysis. Recently, unmanned aerial vehicle (UAV)-aided disaster management has been considered a promising approach to enhance the efficiency of searching and rescuing survivors after a disaster, in which a group of UAVs collaborates to accomplish the search and rescue task. However, the battery capacity of UAVs is a critical shortcoming that limits their usage. Worse still, the unstable network connectivity of disaster sites could lead to high latency of data transmission from UAV to remote data centers, which could make significant challenges on real-time data collecting and processing. To solve the above problems, in this paper, we investigate an energy-efficient multihop data routing algorithm with the guarantee of quality-of-service for UAV-aided medical assistance. Specifically, we first study the data routing problem to minimize the energy consumption considering transmission rate, time delay, and life cycle of the UAV swarms. Then, we formulate the issue as a mixed-integer nonlinear programming model. Because of the Non-deterministic Polynomial-hardness of this problem, we propose a polynomial time algorithm based on a genetic algorithm to solve the problem. To achieve high efficiency, we further enhance our algorithm based on DBSCAN and adaptive techniques. Extensive experiments show that our approach can outperform the state-of-the-art methods.