Sleep stage classification is of great significance to the diagnosis of sleep disorders. However, existing sleep stage classification models based on deep learning are usually relatively large in size (wider and deeper), which makes them hard to be deployed on wearable devices. Therefore, it is a challenge to lighten the existing sleep stage classification models. In this paper, we propose a novel general knowledge distillation framework for sleep stage classification tasks called SleepKD. Our SleepKD, composed of the multi-level module, teacher assistant module, and other knowledge distillation modules, aims to lighten large-scale sleep stage classification models. Specifically, the multi-level module is able to transfer the multi-level knowledge extracted from sleep signals by the teacher model (large-scale model) to the student model (lightweight model). Moreover, the teacher assistant module bridges the large gap between the teacher and student network, and further improves the distillation. We evaluate our method on two public sleep datasets (Sleep-EDF and ISRUC-III). Compared to the baseline methods, the results show that our knowledge distillation framework achieves state-of-the-art performance. SleepKD can significantly lighten the sleep model while maintaining its classification performance. The source code is available at https://github.com/HychaoWang/SleepKD.