Tactile pose estimation and tactile servoing are fundamental capabilities of robot touch. Reliable and precise pose estimation can be provided by applying deep learning models to high-resolution optical tactile sensors. Given the recent successes of Graph Neural Network (GNN) and the effectiveness of Voronoi features, we developed a Tactile Voronoi Graph Neural Network (Tac-VGNN) to achieve reliable pose-based tactile servoing relying on a biomimetic optical tactile sensor (TacTip). The GNN is well suited to modeling the distribution relationship between shear motions of the tactile markers, while the Voronoi diagram supplements this with area-based tactile features related to contact depth. The experiment results showed that the Tac-VGNN model can help enhance data interpretability during graph generation and model training efficiency significantly than CNN-based methods. It also improved pose estimation accuracy along vertical depth by 28.57% over vanilla GNN without Voronoi features and achieved better performance on the real surface following tasks with smoother robot control trajectories. For more project details, please view our website: https://sites.google.com/view/tac-vgnn/home