Spatial transcriptomics (ST) utilizes spatial localization information to profile tissue transcriptomes, presenting substantial computational challenges due to data complexity and high dimensionality. However, conventional dimensionality reduction strategies of such data predicated on Euclidean space often distort spatial distribution and regulatory mechanisms. In this work, we develop HyperDiffuseNet, an innovative deep hyperbolic manifold learning dimensionality reduction method that integrates hyperbolic manifolds with graph diffusion convolutional layers and neural networks to enhance ST data representation. Empirical evaluations on real datasets show that HyperDiffuseNet outperforms traditional dimensionality reduction methods in ST data clustering tasks, elucidating critical biological processes and uncovering pivotal cellular signaling pathways.