In recent years, there has been a significant increase in the demand for unmanned aerial vehicle (UAV)-based monitoring systems to ensure proper emergency response during natural disasters such as wildfires, hurricanes, floods, and earthquakes. This paper proposes a real-time UAV monitoring system for responding to forest fires or floods. The proposed system consists of a hardware part and a software part. The hardware configuration is an embedded camera board mounted on the UAV, a Qualcomm QCS610 SoC with cores suitable for running deep learning-based algorithms. The software configuration is a deep learning-based semantic segmentation model for detecting fires or floods. To execute the model in real time on edge devices with limited resources, we used a network slimming technique which generates a lightweight model with reduced model size, number of parameters, and computational complexity. The performance of the proposed system was evaluated on the FLAME dataset consisting of forest fire images and the FloodNet dataset consisting of flood images. The experimental results showed that the mIoU of slimmed DeepLabV3+ for FLAME is 88.29%, and the inference speed is 10.92 fps. For FloodNet, the mIoU of the slimmed DeepLabV3+ is 94.15%, and the inference speed is 13.26 fps. These experimental results confirm that the proposed system is appropriate for accurate, low-power, real-time monitoring of forest fires and floods using UAVs.