Existing segmentation methods for brain MRI data usually leverage 3D CNNs on 3D volumes or employ 2D CNNs on 2D image slices. We discovered that while volume-based approaches well respect spatial relationships across slices, slice-based methods typically excel at capturing fine local features. Furthermore, there is a wealth of complementary information between their segmentation predictions. Inspired by this observation, we develop an Uncertainty-aware Multi-dimensional Mutual learning framework to learn different dimensional networks simultaneously, each of which provides useful soft labels as supervision to the others, thus effectively improving the generalization ability. Specifically, our framework builds upon a 2D-CNN, a 2.5D-CNN, and a 3D-CNN, while an uncertainty gating mechanism is leveraged to facilitate the selection of qualified soft labels, so as to ensure the reliability of shared information. The proposed method is a general framework and can be applied to varying backbones. The experimental results on three datasets demonstrate that our method can significantly enhance the performance of the backbone network by notable margins, achieving a Dice metric improvement of 2.8% on MeniSeg, 1.4% on IBSR, and 1.3% on BraTS2020.