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Dense prediction in medical volume provides enriched guidance for clinical analysis. CNN backbones have met bottleneck due to lack of long-range dependencies and global context modeling power. Recent works proposed to combine vision transformer with CNN, due to its strong global capture ability and learning capability. However, most works are limited to simply applying pure transformer with several fatal flaws (i.e., lack of inductive bias, heavy computation and little consideration for 3D data). Therefore, designing an elegant and efficient vision transformer learner for dense prediction in medical volume is promising and challenging. In this paper, we propose a novel 3D Shuffle-Mixer network of a new Local Vision Transformer-MLP paradigm for medical dense prediction. In our network, a local vision transformer block is utilized to shuffle and learn spatial context from full-view slices of rearranged volume, a residual axial-MLP is designed to mix and capture remaining volume context in a slice-aware manner, and a MLP view aggregator is employed to project the learned full-view rich context to the volume feature in a view-aware manner. Moreover, an Adaptive Scaled Enhanced Shortcut is proposed for local vision transformer to enhance feature along spatial and channel dimensions adaptively, and a CrossMerge is proposed to skip-connects the multi-scale feature appropriately in the pyramid architecture. Extensive experiments demonstrate the proposed model outperforms other state-of-the-art medical dense prediction methods.