3D point cloud primitive segmentation is pivotal for advancing 3D scene understanding, with the primary challenge arising in unstructured and complex object environments in a zero-shot setting. Current methods often rely on real images or large training datasets, limiting their scalability and generalization. To overcome these limitations, we propose Segment Any Primitive (SAP), the zero-shot 3D primitive segmentation framework that does not rely on real images or training modules. SAP introduces an innovative multiview rendering strategy with dual-feature fusion, establishing precise back-projection relationships between images and point clouds. By incorporating Segment Anything 2 (SAM2) for rendered image segmentation, SAP integrates mask features with geometric priors for fine-grained segmentation, using a hybrid affinity graph-clustering algorithm. Unlike existing approaches, SAP eliminates the need for labor-intensive dataset preparation and parameter tuning, achieving superior generalization to unknown objects and scenes. Experimental results validated through a robust evaluation benchmark, demonstrate that SAP outperforms existing zero-shot methods in key metrics, providing a potential solution for real-world robotic applications.