The analysis of 3D meshes with deep learning has become prevalent in computer graphics. As an essential structure, hierarchical representation is critical for mesh pooling in multiscale analysis. Existing clustering-based mesh hierarchy construction methods involve nonlinear discretization optimization operations, making them nondifferential and challenging to embed in other trainable networks for learning. Inspired by deep superpixel learning methods in image processing, we extend them from 2D images to 3D meshes by proposing a novel differentiable chart-based segmentation method named geodesic differential supervertex (GDSV). The key to the GDSV method is to ensure that the geodesic position updates are differentiable while satisfying the constraint that the renewed supervertices lie on the manifold surface. To this end, in addition to using the differential SLIC clustering algorithm to update the nonpositional features of the supervertices, a reparameterization trick, the Gumbel-Softmax trick, is employed to renew the geodesic positions of the supervertices. Therefore, the geodesic position update problem is converted into a linear matrix multiplication issue. The GDSV method can be an independent module for chart-based segmentation tasks. Meanwhile, it can be combined with the front-end feature learning network and the back-end task-specific network as a plug-in-plug-out module for training; and be applied to tasks such as shape classification, part segmentation, and 3D scene understanding. Experimental results show the excellent performance of our proposed algorithm on a range of datasets.