Efficient evaluation of three-dimensional (3D) medical images is crucial for diagnostic and therapeutic practices in healthcare. Recent years have seen a substantial uptake in applying deep learning and computer vision to analyse and interpret medical images. Traditional approaches, such as convolutional neural networks (CNNs) and vision transformers (ViTs), face significant computational challenges, prompting the need for architectural advancements. Recent efforts have led to the introduction of novel architectures like the ``Mamba'' model as alternative solutions to traditional CNNs or ViTs. The Mamba model excels in the linear processing of one-dimensional data with low computational demands. However, Mamba's potential for 3D medical image analysis remains underexplored and could face significant computational challenges as the dimension increases. This manuscript presents MobileViM, a streamlined architecture for efficient segmentation of 3D medical images. In the MobileViM network, we invent a new dimension-independent mechanism and a dual-direction traversing approach to incorporate with a vision-Mamba-based framework. MobileViM also features a cross-scale bridging technique to improve efficiency and accuracy across various medical imaging modalities. With these enhancements, MobileViM achieves segmentation speeds exceeding 90 frames per second (FPS) on a single graphics processing unit (i.e., NVIDIA RTX 4090). This performance is over 24 FPS faster than the state-of-the-art deep learning models for processing 3D images with the same computational resources. In addition, experimental evaluations demonstrate that MobileViM delivers superior performance, with Dice similarity scores reaching 92.72%, 86.69%, 80.46%, and 77.43% for PENGWIN, BraTS2024, ATLAS, and Toothfairy2 datasets, respectively, which significantly surpasses existing models.