High-quality tabular data is essential for data-driven tasks, yet often limited by scarcity and privacy concerns. While synthetic data generated by recent Deep Generative Models and LLMs improves fidelity, existing methods struggle to preserve rigorous attribute dependencies. As a result, the generated data may appear statistically realistic but lack logical consistency. To address this challenge, we propose CauTab, a novel counterfactual framework for tabular data synthesis that preserves functional dependencies and causal-dependency structures. CauTab operates in a three-stage pipeline: (1) it employs an LLM-guided mining strategy to efficiently identify functional dependencies; (2) it constructs a causal-dependency graph by integrating data-driven optimization with LLM-based semantic reasoning; and (3) it executes a dependency-constrained generation process via the Abduction-Intervention-Prediction paradigm. By enforcing deterministic constraints and using the learned graph for structured propagation, CauTab improves statistical fidelity while preserving logical consistency. Experiments demonstrate that CauTab outperforms baselines in data utility and fidelity, while maintaining competitive empirical privacy and strong logical consistency.