State-of-the-art Graph Neural Networks (GNNs) have limited scalability with respect to the graph and model sizes. On large graphs, increasing the model depth often means exponential expansion of the receptive field (i.e., scope). Beyond just a few layers, two fundamental challenges emerge: 1. degraded expressivity due to oversmoothing, and 2. expensive computation due to neighborhood explosion. We propose a design principle to decouple the depth and scope of GNNs – to generate representation of a target entity (i.e., a node or an edge), we first extract a localized subgraph as the bounded-size receptive field, and then apply a GNN of arbitrary depth on top of the subgraph. A properly extracted subgraph consists of a small number of critical neighbors, while excluding irrelevant ones. The GNN, no matter how deep it is, smooths the local signals into informative representation without oversmoothing the global graph into ”white noise”. Theoretically, such decoupling improves the expressive power of popular GNN architectures, including GCN, GraphSAGE and GIN. Empirically, on seven graphs (up to 110M nodes) and six backbone GNN architectures, our design achieves state-of-the-art accuracy with an order of magnitude reduction in computation and hardware cost.