Distillation-aware Architecture Search (DAS) seeks to discover the ideal student architecture that delivers superior performance by distilling knowledge from a given teacher model. Previous DAS methods involve time-consuming training-based search processes. Recently, the training-free DAS method (\ie, DisWOT) proposes KD-based proxies and achieves significant search acceleration. However, we observe that DisWOT suffers from limitations such as the need for manual design and poor generalization to diverse architectures, such as the Vision Transformer (ViT). To address these issues, we present Auto-DAS, an automatic proxy discovery framework using an Evolutionary Algorithm (EA) for training-free DAS. Specifically, we empirically find that proxies conditioned on student instinct statistics and teacher-student interaction statistics can effectively predict distillation accuracy. Then, we represent the proxy with computation graphs and construct the proxy search space using instinct and interaction statistics as inputs. To identify promising proxies, our search space incorporates various types of basic transformations and network distance operators inspired by previous proxy and KD-loss designs. Next, our EA initializes populations, evaluates, performs crossover and mutation operations, and selects the best correlation candidate with distillation accuracy. We introduce an adaptive-elite selection strategy to enhance search efficiency and strive for a balance between exploitation and exploration. Finally, we conduct training-free DAS with discovered proxy before the optimal student distillation phase. In this way, our auto-discovery framework eliminates the need for manual design and tuning, while also adapting to different search spaces through direct correlation optimization. Extensive experiments demonstrate that Auto-DAS generalizes well to various architectures and search spaces (\eg, ResNet, ViT, NAS-Bench-101, and NAS-Bench-201), achieving state-of-the-art results in both ranking correlation and final searched accuracy. Code is included in the supplementary materials.