Synthetic Aperture Radar (SAR) image registration is an essential upstream task in geoscience applications, in which pre-detected keypoints from two images are employed as observed objects to seek matched-point pairs. In general, the registration is regarded as a typical closed-set classification, which forces each keypoint to be classified into the given classes, but ignoring an essential issue that numerous redundant keypoints are beyond the given classes, which unavoidably results in capturing incorrect matched-point pairs. Based on this, we propose a Cross-Rejective Open-set SAR Image Registration (CroR-OSIR) method. In this work, these redundant keypoints are regarded as out-of-distribution (OOD) samples, and we formulate the registration as a special open-set task with two modules: supervised contrastive feature-tuning and cross-rejective open-set recognition (CroR-OSR). Different from traditional open set recognition, all samples including OOD samples are available in the CroR-OSR module. CroR-OSR conducts the closed-set classifications in individual open-set domains from two images, meanwhile employing the cross-domain rejection during training, to exclude these OOD samples based on confidence and consistency. Moreover, a new supervised contrastive tuning strategy is incorporated for feature-tuning. Especially, the cross-domain estimation labels obtained by CroR-OSR are fed back to the feature-tuning module for feature-tuning, to enhance feature discriminability. Experimental results indicate that the proposed method achieves more precise registration than the state-of-the-art methods.