I'm wondering what benchmarks there exist for semantic segmentation of 3D meshes? I have already found "A Benchmark for 3D Mesh Segmentation"; is this currently the only benchmark that exists for 3D mesh segmentation?
The one you are refering to is the common PSB (Princeton Segmentation Benchmark) dataset . Other Important datasets used for 3D mesh segmentation are:
- COSEG 
- ShapeNet 
- Other from Princeton 
- Other basen on subset of ShapeNet 
On the other hand, there seems to be no state-of-the-art page for 3D shape segmentation. But the papers I find most important are [6, 7, 8, 9], with 9 the state of the art.
- Chen et al: A Benchmark for 3D Mesh Segmentation, 2009
- Wang et al: Active co-analysis of a set of shapes, 2012
- Kim et al: Learning Part-based Templates from Large Collections of 3D Shapes, 2013
- Chang et al: ShapeNet: An Information-Rich 3D Model Repository, 2015
- Yi et al: A scalable active framework for region annotation in 3d shape collections, 2016
- Kalogerakis et al: Learning 3D Mesh Segmentation and Labeling, 2010
- Guo et al: 3D Mesh Labeling via Deep Convolutional Neural Networks, 2015
- Kalogerakis et al: 3D Shape Segmentation with Projective Convolutional Networks, 2017
- Wang et al: 3D shape segmentation via shape fully convolutional networks, 2018