Dynamic 3D scene reconstruction is essential for immersive media such as VR, MR, and XR, yet remains challenging for long multi-view sequences with large-scale motion. Existing dynamic Gaussian approaches are either Frame-Stream, offering scalability but poor temporal stability, or Clip, achieving local consistency at the cost of high memory and limited sequence length. We propose ClipGStream, a hybrid reconstruction framework that performs stream optimization at the clip level rather than the frame level. The sequence is divided into short clips, where dynamic motion is modeled using clip-independent spatio-temporal fields and residual anchor compensation to capture local variations efficiently, while inter-clip inherited anchors and decoders maintain structural consistency across clips. This Clip-Stream design enables scalable, flicker-free reconstruction of long dynamic videos with high temporal coherence and reduced memory overhead. Extensive experiments demonstrate that ClipGStream achieves state-of-the-art reconstruction quality and efficiency. The project page is available at: https://liangjie1999.github.io/ClipGStreamWeb/