Dynamic 3D reconstruction of surgical scenes plays a critical role in robotic-assisted surgery. Gaussian Splatting (GS), while effective for novel view synthesis, struggles to recover accurate surface from a monocular view due to the implicit multi-Gaussian representation of the surface. Specifically, (1) the vertical overlap of Gaussians leads to floating artifacts, and (2) the random orientation of Gaussians affects the smoothness of the reconstructed surface. Consequently, these fragmented and misaligned Gaussians hinder downstream applications, e.g., geometry-aware endoscopic navigation and physics-integrated tissue mechanics simulation. To this end, we propose Endo-GSG, a unified framework that couples dynamic Gaussian splatting with an SDF field for dynamic surface-aware tissue reconstruction. To further enhance geometric fidelity, we design geometry-informed regularization losses that constrain Gaussian density and spatial positioning. The entire pipeline is jointly supervised by RGB images and predicted depth maps, enabling high-quality reconstruction and rendering even with sparse or monocular input. Experiments on public datasets demonstrate that Endo-GSG outperforms state-of-the-art methods in both rendering quality and geometric surface accuracy.