Despite rapid progress, embodied agents still struggle with long-horizon manipulation that requires maintaining spatial consistency, causal dependencies, and goal constraints. A key limitation of existing approaches is that task reasoning is implicitly embedded in high-dimensional latent representations, making it challenging to separate task structure from perceptual variability. We introduce Grounded Scene-graph Reasoning (GSR), a structured reasoning paradigm that explicitly models world-state evolution as transitions over semantically grounded scene graphs. By reasoning step-wise over object states and spatial relations, rather than directly mapping perception to actions, GSR enables explicit reasoning about action preconditions, consequences, and goal satisfaction in a physically grounded space. To support learning such reasoning, we construct Manip-Cognition-1.6M, a large-scale dataset that jointly supervises world understanding, action planning, and goal interpretation. Extensive evaluations across RLBench, LIBERO, GSR-benchmark, and real-world robotic tasks show that GSR significantly improves zero-shot generalization and long-horizon task completion over prompting-based baselines. These results highlight explicit world-state representations as a key inductive bias for scalable embodied reasoning.