Though U-Net has achieved tremendous success in medical image segmentation tasks, it lacks the ability to explicitly model long-range dependencies. Therefore, Vision Transformers have emerged as alternative segmentation structures recently, for their innate ability of capturing long-range correlations through Self-Attention (SA). However, Transformers usually rely on large-scale pre-training and have high computational complexity. Furthermore, SA can only model self-affinities within a single sample, ignoring the potential correlations of the overall dataset. To address these problems, we propose a novel Transformer module named Mixed Transformer Module (MTM) for simultaneous inter- and intra- affinities learning. MTM first calculates self-affinities efficiently through our well-designed Local-Global Gaussian-Weighted Self-Attention (LGG-SA). Then, it mines inter-connections between data samples through External Attention (EA). By using MTM, we construct a U-shaped model named Mixed Transformer U-Net (MT-UNet) for accurate medical image segmentation. We test our method on two different public datasets, and the experimental results show that the proposed method achieves better performance over other state-of-the-art methods. The code is available at: https://github.com/Dootmaan/MT-UNet.