While 3D Gaussian Splatting has shown promising results in street scene reconstruction, existing methods require massive numbers of Gaussian primitives to capture fine details, leading to prohibitive storage costs and slow rendering speeds. We observe that dynamic objects (e.g., vehicles and pedestrians) demand high-fidelity representations to maintain temporal consistency, while static background regions often contain substantial redundancy. Motivated by this, we propose SparseStreet, a general compression framework specifically designed for street scenes. First, we introduce a node-based learnable pruning strategy that systematically removes low-contributing Gaussian primitives while preserving visually critical regions. Second, after the scene representation stabilizes, we apply background compression, further reducing redundancy in static regions. Our method effectively preserves the geometry and appearance of dynamic objects while significantly reducing the total number of Gaussian primitives. Extensive experiments on the Waymo and nuScenes demonstrate that SparseStreet achieves up to 80% compression ratio with minimal quality degradation, enabling resource-efficient, high-fidelity dynamic scene reconstruction. Project website: https://sparsestreet.github.io/.