The usage of Multi Instance Learning (MIL) for classifying Whole Slide Images (WSIs) has recently increased. Due to their gigapixel size, the pixel-level annotation of such data is extremely expensive and timeconsuming, practically unfeasible. For this reason, multiple automatic approaches have been raised in the last years to support clinical practice and diagnosis. Unfortunately, most state-of-the-art proposals apply attention mechanisms without considering the spatial instance correlation and usually work on a single-scale resolution. To leverage the full potential of pyramidal structured WSI, we propose a graph-based multi-scale MIL approach, DAS-MIL. Our model comprises three modules: i) a self-supervised feature extractor, ii) a graph-based architecture that precedes the MIL mechanism and aims at creating a more contextualized representation of the WSI structure by considering the mutual (spatial) instance correlation both inter and intra-scale. Finally, iii) a (self) distillation loss between resolutions is introduced to compensate for their informative gap and significantly improve the final prediction. The effectiveness of the proposed framework is demonstrated on two well-known datasets, where we outperform SOTA on WSI classification, gaining a +2.7% AUC and +3.7% accuracy on the popular Camelyon16 benchmark.