Multi-instance point cloud registration estimates the poses of multiple source point cloud instances in a target point cloud. Solving this problem relies on first extracting point correspondences. However, existing methods treat the target point cloud as a whole, neglecting the independence of instances. As a result, point features could be easily poluted by those from background or other instances, leading to inaccurate correspondences and missing instances, especially in cluttered scenes. In this work, we propose Multi-Instance REgistration TRansformer, a coarse-to-fine framework to directly extract correspondences and estimate the transformation for each instance. In the coarse level, our method jointly learns instance-aware superpoint features and predicts local instance masks. Benefiting from the instance masks, the influence from outside of instance is alleviated, such that highly reliable superpoint correspondences are extracted. The superpoint correspondences are further extended to instance candidates in the fine level according to the instance masks. At last, an efficient candidate selection and refinement algorithm is devised to obtain the final registrations. Extensive experiments on two benchmarks have demonstrated the efficacy of our design. MIRETR outperforms the previous state-of-the-art by over 30.22 points on F1 score on the challenging ROBI benchmark. Our code and models will be released.