We propose an algorithm, namely 4DRegSDF, for spacetime surface regularization to improve the fidelity of 4D rendering and reconstruction in dynamic scenes. Recent progress in the field has focused mainly on photometric quality, resulting in sub-optimal shape reconstruction quality. To address this issue, we adopt a decomposed 4D representation for the motion and Signed Distance Function (SDF) geometry model. Our approach involves (1) sampling points on the deformed surface by taking a gradient step toward the steepest direction along SDF and (2) extracting differential surface geometry, such as tangent plane or curvature, for motion regularization. These properties enable our dynamic surface regularization technique to minimize energy term and align 4D spacetime geometry via 3D canonical space. Experiments demonstrate that our 4DRegSDF achieves state-of-the-art performance in both reconstruction and rendering quality over synthetic and real-world datasets. We will open-source the code for reproducibility.