Reconstructing dynamic 3D scenes from monocular videos remains a fundamental challenge in 3D vision. While 3D Gaussian Splatting (3DGS) achieves real-time rendering in static settings, extending it to dynamic scenes is challenging due to the difficulty of learning structured and temporally consistent motion representations. This challenge often manifests as three limitations in existing methods: redundant Gaussian updates, insufficient motion supervision, and weak modeling of complex non-rigid deformations. These issues collectively hinder coherent and efficient dynamic reconstruction. To address these limitations, we propose HAIF-GS, a unified framework that enables structured and consistent dynamic modeling through sparse anchor-driven deformation. It first identifies motion-relevant regions via an Anchor Filter to suppress redundant updates in static areas. A self-supervised Induced Flow-Guided Deformation module induces anchor motion using multi-frame feature aggregation, eliminating the need for explicit flow labels. To further handle fine-grained deformations, a Hierarchical Anchor Propagation mechanism increases anchor resolution based on motion complexity and propagates multi-level transformations. Extensive experiments on synthetic and real-world benchmarks validate that HAIF-GS significantly outperforms prior dynamic 3DGS methods in rendering quality, temporal coherence, and reconstruction efficiency.