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Among various sensors for assisted and autonomous driving systems, automotive radar has been considered as a robust and low-cost solution even in adverse weather or lighting conditions. With the recent development of radar technologies and open-sourced annotated data sets, semantic segmentation with radar signals has become very promising. However, existing methods are either computationally expensive or discard significant amounts of valuable information from raw 3D radar signals by reducing them to 2D planes via averaging. In this work, we introduce ERASE-Net, an Efficient RAdar SEgmentation Network to segment the raw radar signals semantically. The core of our approach is the novel detect-then-segment method for raw radar signals. It first detects the center point of each object, then extracts a compact radar signal representation, and finally performs semantic segmentation. We show that our method can achieve superior performance on radar semantic segmentation task compared to the state-of-the-art (SOTA) technique. Furthermore, our approach requires up to 20x less computational resources. Finally, we show that the proposed ERASE-Net can be compressed by 40% without significant loss in performance, significantly more than the SOTA network, which makes it a more promising candidate for practical automotive applications.