Accurate and automated segmentation of 3D biomedical images is a sophisticated imperative in clinical diagnosis, imaging-guided surgery, and prognosis judgment. Although the burgeoning of deep learning technologies has fostered smart segmentators, the successive and simultaneous garnering global and local features still remains challenging, which is essential for an exact and efficient imageological assay. To this end, a segmentation solution dubbed the mixed parallel shunted transformer (MPSTrans) is developed here, highlighting 3D-MPST blocks in a U-form framework. It enabled not only comprehensive characteristic capture and multiscale slice synchronization but also deep supervision in the decoder to facilitate the fetching of hierarchical representations. Performing on an unpublished colon cancer data set, this model achieved an impressive increase in dice similarity coefficient (DSC) and a 1.718 mm decease in Hausdorff distance at 95% (HD95), alongside a substantial shrink of computational load of 56.7% in giga floating-point operations per second (GFLOPs). Meanwhile, MPSTrans outperforms other mainstream methods (Swin UNETR, UNETR, nnU-Net, PHTrans, and 3D U-Net) on three public multiorgan (aorta, gallbladder, kidney, liver, pancreas, spleen, stomach, etc.) and multimodal (CT, PET-CT, and MRI) data sets of medical segmentation decathlon (MSD) brain tumor, multiatlas labeling beyond cranial vault (BCV), and automated cardiac diagnosis challenge (ACDC), accentuating its adaptability. These results reflect the potential of MPSTrans to advance the state-of-the-art in biomedical imaging analysis, which would offer a robust tool for enhanced diagnostic capacity.