Progress in digital pathology is hindered by highresolution images and the prohibitive cost of exhaustive localized annotations. The commonly used paradigm to categorize pathology images is patch-based processing, which often incorporates multiple instance learning (MIL) to aggregate local patch-level representations yielding imagelevel prediction. Nonetheless, diagnostically relevant regions may only take a small fraction of the whole tissue, and MIL-based aggregation operation assumes that all patch representations are independent and thus mislays the contextual information from adjacent cell and tissue microenvironments. Consequently, the computational resources dedicated to a specific region are independent of its information contribution. This paper proposes a transformer-based architecture specifically tailored for histopathological image classification, which combines fine-grained local attention with a coarse global attention mechanism to learn meaningful representations of high-resolution images at an efficient computational cost. More importantly, based on the observation above, we propose a novel mixing-based dataaugmentation strategy, namely ScoreMix, by leveraging the distribution of the semantic regions of images during the training and carefully guiding the data mixing via sampling the locations of discriminative image content. Thorough experiments and ablation studies on three challenging representative cohorts of Haematoxylin & Eosin (H&E) tumour regions-of-interest (TRoIs) datasets have validated the superiority of our approach over existing state-of-theart methods and effectiveness of our proposed components, e.g., data augmentation in improving classification performance. We also demonstrate our method's interpretability, robustness, and cross-domain generalization capability.