With the development of deep convolutional neural networks, medical image segmentation has achieved a series of breakthroughs in recent years. However, the higher-performance convolutional neural networks always mean numerous parameters and high computation costs, which will hinder the applications in clinical scenarios. Meanwhile, the scarceness of large-scale annotated medical image datasets further impedes the application of high-performance networks. To tackle these problems, we propose Graph Flow, a comprehensive knowledge distillation framework, for both network-efficiency and annotation-efficiency medical image segmentation. Specifically, our core Graph Flow Distillation transfer the essence of cross-layer variations from a well-trained cumbersome teacher network to a non-trained compact student network. In addition, an unsupervised Paraphraser Module is designed to purify the knowledge of the teacher network, which is also beneficial for the stabilization of training procedure. Furthermore, we build a unified distillation framework by integrating the adversarial distillation and the vanilla logits distillation, which can further refine the final predictions of the compact network. Extensive experiments conducted on Gastric Cancer Segmentation Dataset and Synapse Multi-organ Segmentation Dataset demonstrate the prominent ability of our method which achieves state-of-the-art performance on these differentmodality and multi-category medical image datasets. Moreover, we demonstrate the effectiveness of our Graph Flow through a new semi-supervised paradigm for dual efficient medical image segmentation. Our code will be available at Graph Flow .