Brain stroke lesion segmentation is of great importance for stroke rehabilitation neuroimaging analysis. Due to the large variance of stroke lesion shapes and similarities of tissue intensity distribution, it remains a challenging task. To help detect abnormalities, the anatomical symmetries of brain magnetic resonance (MR) images have been widely used as visual cues for clinical practices. However, most methods for brain images segmentation do not fully utilize structural symmetry information. This paper presents a novel mirror difference aware network (MDAN) for stroke lesion segmentation. The network uses an encoder-decoder architecture, aiming at holistically exploiting the symmetries of image features. Specifically, a differential feature augmentation (DFA) module is developed in the encoding path to highlight the semantically pathological asymmetries of features in abnormalities. In the DFA module, a Siamese contrastive supervised loss is designed to enhance discriminative features, and a mirror position-based difference augmentation (MDA) module is used to further magnify the discrepancy. Moreover, mirror feature fusion (MFF) modules are applied to efficiently fuse and transfer the information both of the original input and the horizontally flipped features to the decoding path. Extensive experiments on the Anatomical Tracings of Lesions After Stroke (ATLAS) dataset show the proposed MDAN outperforms the state-of-the-art methods.