The balance between high accuracy and high speed has always been a challenging task in semantic image segmentation. Compact segmentation networks are more widely used in the case of limited resources, while their performances are constrained. In this paper, motivated by the residual learning and global aggregation, we propose a simple yet general and effective knowledge distillation framework called double similarity distillation (DSD) to improve the classification accuracy of all existing compact networks by capturing the similarity knowledge in pixel and category dimensions, respectively. Specifically, we propose a pixel-wise similarity distillation (PSD) module that utilizes residual attention maps to capture more detailed spatial dependencies across multiple layers. Compared with exiting methods, the PSD module greatly reduces the amount of calculation and is easy to expand. Furthermore, considering the differences in characteristics between semantic segmentation task and other computer vision tasks, we propose a category-wise similarity distillation (CSD) module, which can help the compact segmentation network strengthen the global category correlation by constructing the correlation matrix. Combining these two modules, DSD framework has no extra parameters and only a minimal increase in FLOPs. Extensive experiments on four challenging datasets, including Cityscapes, CamVid, ADE20K, and Pascal VOC 2012, show that DSD outperforms current state-of-the-art methods, proving its effectiveness and generality. The code and models will be publicly available.