Semantic Scene Completion (SSC) aims to jointly generate space occupancies and semantic labels for complex 3D scenes. Most existing SSC models focus on volumetric representations, which are memory-inefficient for large outdoor spaces. Point clouds provide a lightweight alternative but existing benchmarks lack outdoor point cloud scenes with semantic labels. To address this, we introduce PointSSC, the first cooperative vehicle-infrastructure point cloud benchmark for semantic scene completion. These scenes exhibit long-range perception and minimal occlusion. We develop an automated annotation pipeline leveraging Segment Anything to efficiently assign semantics. To benchmark progress, we propose a LiDAR-based model with a Spatial-Aware Transformer for global and local feature extraction and a Completion and Segmentation Cooperative Module for joint completion and segmentation. PointSSC provides a challenging testbed to drive advances in semantic point cloud completion for real-world navigation.