Volumetric video has emerged as a key medium for immersive telepresence and augmented/virtual reality, enabling six-degrees-of-freedom (6DoF) navigation and realistic spatial interactions. However, delivering high-quality dynamic volumetric content at scale remains challenging due to massive data volume, complex motion, and limited editability of existing representations. In this paper, we present 4D-MoDe, a motion-decoupled 4D Gaussian compression framework designed for scalable and editable volumetric video streaming. Our method introduces a layered representation that explicitly separates static backgrounds from dynamic foregrounds using a lookahead-based motion decomposition strategy, significantly reducing temporal redundancy and enabling selective background/foreground streaming. To capture continuous motion trajectories, we employ a multi-resolution motion estimation grid and a lightweight shared MLP, complemented by a dynamic Gaussian compensation mechanism to model emergent content. An adaptive grouping scheme dynamically inserts background keyframes to balance temporal consistency and compression efficiency. Furthermore, an entropy-aware training pipeline jointly optimizes the motion fields and Gaussian parameters under a rate-distortion (RD) objective, while employing range-based and KD-tree compression to minimize storage overhead. Extensive experiments on multiple datasets demonstrate that 4D-MoDe consistently achieves competitive reconstruction quality with an order of magnitude lower storage cost (e.g., as low as \textbf{11.4} KB/frame) compared to state-of-the-art methods, while supporting practical applications such as background replacement and foreground-only streaming.