Reconstructing general dynamic scenes is important for many computer vision and graphics applications. Recent works represent the dynamic scene with neural radiance fields for photorealistic view synthesis, while their surface geometry is under-constrained and noisy. Other works introduce surface constraints to the implicit neural representation to disentangle the ambiguity of geometry and appearance field for static scene reconstruction. To bridge the gap between rendering dynamic scenes and recovering static surface geometry, we propose a template-free method to reconstruct surface geometry and appearance using neural implicit representations from multi-view videos. We leverage topology-aware deformation and the signed distance field to learn complex dynamic surfaces via differentiable volume rendering without scene-specific prior knowledge like template models. Furthermore, we propose a novel mask-based ray selection strategy to significantly boost the optimization on challenging time-varying regions. Experiments on different multi-view video datasets demonstrate that our method achieves high-fidelity surface reconstruction as well as photorealistic novel view synthesis.