Many emerging user-facing services adopt Graph Neural Networks (GNNs) to improve serving accuracy. When the graph used by a GNN model changes, representations (embedding) of nodes in the graph should be updated accordingly. However, the node representation update is too slow, resulting in either long response latency of user queries (the inference is performed after the update completes) or high staleness problem (the inference is performed based on stale data). Our in-depth analysis shows that the slow update is mainly due to neighbor explosion problem in graphs and duplicated computation. Based on such findings, we propose STAG, a GNN serving framework that enables low latency and low staleness of GNN-based services. It comprises a collaborative serving mechanism and an additivity-based incremental propagation strategy. With the collaborative serving mechanism, only part of node representations are updated during the update phase, and the final representations are calculated in the inference phase. It alleviates the neighbor explosion problem. The additivity-based incremental propagation strategy reuses intermediate data during the update phase, eliminating duplicated computation problem. Experimental results show that STAG accelerates the update phase by 1.3x~90.1x, and greatly reduces staleness time with a slight increase in response latency.