Generating compact and sharply detailed 3D meshes poses a significant challenge for current 3D generative models. Different from extracting dense meshes from neural representation, some recent works try to model the native mesh distribution (i.e., a set of triangles), which generates more compact results as humans crafted. However, due to the complexity and variety of mesh topology, most of these methods are typically limited to generating meshes with simple geometry. In this paper, we introduce a generic and scalable mesh generation framework PivotMesh, which makes an initial attempt to extend the native mesh generation to large-scale datasets. We employ a transformer-based autoencoder to encode meshes into discrete tokens and decode them from face level to vertex level hierarchically. Subsequently, to model the complex typology, our model first learns to generate pivot vertices as coarse mesh representation and then generate the complete mesh tokens with the same auto-regressive Transformer. This reduces the difficulty compared with directly modeling the mesh distribution and further improves the model controllability. PivotMesh demonstrates its versatility by effectively learning from both small datasets like Shapenet, and large-scale datasets like Objaverse and Objaverse-xl. Extensive experiments indicate that PivotMesh can generate compact and sharp 3D meshes across various categories, highlighting its great potential for native mesh modeling.