Link prediction on graphs is a fundamental problem in graph representation learning. Subgraph representation learning approaches (SGRLs), by transforming link prediction to graph classification on the subgraphs around the target links, have advanced the learning capability of Graph Neural Networks (GNNs) for link prediction. Despite their state-of-the-art performance, SGRLs are computationally expensive, and not scalable to large-scale graphs due to their expensive subgraph-level operations for each target link. To unlock the scalability of SGRLs, we propose a new class of SGRLs, that we call Scalable Simplified SGRL (S3GRL). Aimed at faster training and inference, S3GRL simplifies the message passing and aggregation operations in each link's subgraph. S3GRL, as a scalability framework, flexibly accommodates various subgraph sampling strategies and diffusion operators to emulate computationally-expensive SGRLs. We further propose and empirically study multiple instances of S3GRL. Our extensive experiments demonstrate that the proposed S3GRL models scale up SGRLs without any significant performance compromise (even with considerable gains in some cases), while offering substantially lower computational footprints (e.g., multi-fold inference and training speedup). 1