Operator fusion is essentially and widely used in a large number of matrix computation systems in science and industry. The existing distributed operator fusion methods focus on only either low communication cost with the risk of out of memory or large-scale processing with high communication cost. We propose a distributed elastic fused operator called Cuboid-based Fused Operator (CFO) that achieves both low communication cost and large-scale processing. We also propose a novel fusion plan generator called Cuboid-based Fusion plan Generator (CFG) that finds a fusion plan to fuse more operators including large-scale matrix multiplication. We implement a fast distributed matrix computation engine called FuseME by integrating both CFO and CFG seamlessly. FuseME outperforms the state-of-the-art systems including SystemDS by orders of magnitude.