In this work, we address 3D novel class discovery (NCD) that discovers novel classes from an unlabeled dataset by leveraging the knowledge of disjoint known classes. The key challenge of 3D NCD is that learned features by known class recognition are heavily biased and hinder generalization to novel classes. Since geometric parts are more generalizable across different classes, we propose to decompose novel into known parts, coined DNIK, to mitigate the above problems. DNIK learns a part concept bank encoding rich part geometric patterns from known classes so that novel 3D shapes can be represented as part concept compositions to facilitate cross-category generalization. Moreover, we formulate three constraints on part concepts to ensure diverse part concepts without collapsing. A part relation encoding module (PRE) is also developed to leverage part-wise spatial relations for better recognition. We construct three 3D NCD tasks for evaluation and extensive experiments show that our method achieves significantly superior results than SOTA baselines (+11.7%, +14.1%, and +16.3% improvements on average for three tasks, respectively). Code and data will be released.