We are in the era of millimetre-scale electron microscopy volumes collected at nanometre resolution. Dense reconstruction of cellular compartments in these electron microscopy volumes has been enabled by recent advances in machine learning. Automated segmentation methods produce exceptionally accurate reconstructions of cells, but post hoc proofreading is still required to generate large connectomes that are free of merge and split errors. The elaborate 3D meshes of neurons in these volumes contain detailed morphological information at multiple scales, from the diameter, shape and branching patterns of axons and dendrites, down to the fine-scale structure of dendritic spines. However, extracting these features can require substantial effort to piece together existing tools into custom workflows. Here, building on existing open source software for mesh manipulation, we present Neural Decomposition (NEURD), a software package that decomposes meshed neurons into compact and extensively annotated graph representations. With these feature-rich graphs, we automate a variety of tasks such as state-of-the-art automated proofreading of merge errors, cell classification, spine detection, axonal-dendritic proximities and other annotations. These features enable many downstream analyses of neural morphology and connectivity, making these massive and complex datasets more accessible to neuroscience researchers.