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Deep-learning based speech separation models confront poor generalization problem that even the state-of-the-art models could abruptly fail when evaluating them in mismatch conditions. To address this problem, we propose an easy-to-implement yet effective consistency based semi-supervised learning (SSL) approach, namely Mixup-Breakdown training (MBT). It learns a teacher model to "breakdown" unlabeled inputs, and the estimated separations are interpolated to produce more useful pseudo "mixup" input-output pairs, on which the consistency regularization could apply for learning a student model. In our experiment, we evaluate MBT under various conditions with ascending degrees of mismatch, including unseen interfering speech, noise, and music, and compare MBT's generalization capability against state-of-the-art supervised learning and SSL approaches. The result indicates that MBT significantly outperforms several strong baselines with up to 13.77% relative SI-SNRi improvement. Moreover, MBT only adds negligible computational overhead to standard training schemes.