This paper tackles a new problem of dataset pruning for Knowledge Distillation (KD), from a fresh perspective of Decision Boundary (DB) preservation and drifts. Existing dataset pruning methods generally assume that the post-pruning DB formed by the selected samples can be well-captured by future networks that use those samples for training. Therefore, they tend to preserve hard samples since hard samples are closer to the DB and better characterize the nuances in the distribution of the entire dataset. However, in KD, the limited learning capacity from the student network leads to imperfect preservation of the teacher's feature distribution, resulting in the drift of DB in the student space. Specifically, hard samples worsen such drifts as they are difficult for the student to learn, creating a situation where the student's DB can drift deeper into other classes and make incorrect classifications. Motivated by these findings, our method selects medium-difficulty samples for KD-based dataset pruning. We show that these samples constitute a smoothed version of the teacher's DB and are easier for the student to learn, obtaining a general feature distribution preservation for a class of samples and reasonable DB between different classes for the student. In addition, to reduce the distributional shift due to dataset pruning, we leverage the class-wise distributional information of the teacher's outputs to reshape the logits of the preserved samples. Experiments show that the proposed static pruning method can even perform better than the state-of-the-art dynamic pruning method which needs access to the entire dataset. In addition, our method halves the training times of KD and improves the student's accuracy by 0.4% on ImageNet with a 50% keep ratio. When the ratio further increases to 70%, our method achieves higher accuracy over the vanilla KD while reducing the training times by 30%. Code is available at https://github.com/chenyd7/MDSLR.