Entity alignment (EA) aims at finding equivalent entities in different knowledge graphs (KGs). Embedding-based approaches have dominated the EA task in recent years. Those methods face problems that come from the geometric properties of embedding vectors, including hubness and isolation. To solve these geometric problems, many normalization approaches have been adopted for EA. However, the increasing scale of KGs renders it hard for EA models to adopt the normalization processes, thus limiting their usage in real-world applications. To tackle this challenge, we present ClusterEA, a general framework that is capable of scaling up EA models and enhancing their results by leveraging normalization methods on mini-batches with a high entity equivalent rate. ClusterEA contains three components to align entities between large-scale KGs, including stochastic training, ClusterSampler, and SparseFusion. It first trains a large-scale Siamese GNN for EA in a stochastic fashion to produce entity embeddings. Based on the embeddings, a novel ClusterSampler strategy is proposed for sampling highly overlapped mini-batches. Finally, ClusterEA incorporates SparseFusion, which normalizes local and global similarity and then fuses all similarity matrices to obtain the final similarity matrix. Extensive experiments with real-life datasets on EA benchmarks offer insight into the proposed framework, and suggest that it is capable of outperforming the state-of-the-art scalable EA framework by up to 8 times in terms of Hits@1.