We address the over-constrained planning problem in semi-static environments. The planning objective is to find a best-effort solution that avoids all hard constraint regions while minimally traversing the least risky areas. Conventional methods often rely on pre-defined area costs, limiting generalizations. Further, the spatial continuity of navigation spaces makes it difficult to identify regions that are passable without overestimation. To overcome these challenges, we propose SuReNav, a superpixel graph-based constraint relaxation and navigation method that imitates human-like safe and efficient navigation. Our framework consists of three components: 1) superpixel graph map generation with regional constraints, 2) regional-constraint relaxation using graph neural network trained on human demonstrations for safe and efficient navigation, and 3) interleaving relaxation, planning, and execution for complete navigation. We evaluate our method against state-of-the-art baselines on 2D semantic maps and 3D maps from OpenStreetMap, achieving the highest human-likeness score of complete navigation while maintaining a balanced trade-off between efficiency and safety. We finally demonstrate its scalability and generalization performance in real-world urban navigation with a quadruped robot, Spot. Code and Videos are available at https://sure-nav.github.io/.