GAN-based facial attribute editing is widely used in virtual avatars and social media but often suffers from attribute entanglement, where modifying one face attribute unintentionally alters others. While supervised disentangled representation learning can address this, it relies heavily on labeled data, incurring high annotation costs. To address these challenges, we propose MD-Face, a label-free disentangled representation learning framework based on Mixture of Experts (MoE). MD-Face utilizes a MoE backbone with a gating mechanism that dynamically allocates experts, enabling the model to learn semantic vectors with greater independence. To further enhance attribute entanglement, we introduce a geometry-aware loss, which aligns each semantic vector with its corresponding Semantic Boundary Vector (SBV) through a Jacobian-based pushforward method. Experiments with ProGAN and StyleGAN show that MD-Face outperforms unsupervised baselines and competes with supervised ones. Compared to diffusion-based methods, it offers better image quality and lower inference latency, making it ideal for interactive editing.