Large language models (LLMs) have achieved promising results in tabular data generation. However, inherent historical biases in tabular datasets often cause LLMs to exacerbate fairness issues, particularly when multiple advantaged and protected features are involved. In this work, we introduce a universal debiasing framework that minimizes group-level dependencies by simultaneously reducing the mutual information between advantaged and protected attributes. By leveraging the autoregressive structure and analytic sampling distributions of LLM-based tabular data generators, our approach efficiently computes mutual information, reducing the need for cumbersome numerical estimations. Building on this foundation, we propose two complementary methods: a direct preference optimization (DPO)-based strategy, namely UDF-DPO, that integrates seamlessly with existing models, and a targeted debiasing technique, namely UDF-MIX, that achieves debiasing without tuning the parameters of LLMs. Extensive experiments demonstrate that our framework effectively balances fairness and utility, offering a scalable and practical solution for debiasing in high-stakes applications.