In code vulnerability detection tasks, a detector trained on a label-rich source domain fails to provide accurate prediction on new or unseen target domains due to the lack of labeled training data on target domains. Previous studies mainly utilize domain adaptation to perform cross-domain vulnerability detection. But they ignore the negative effect of private semantic characteristics of the target domain for domain alignment, which easily causes the problem of negative transfer. In addition, these methods forcibly reduce the distribution discrepancy between domains and do not take into account the interference of irrelevant target instances for distributional domain alignment, which leads to the problem of excessive alignment. To address the above issues, we propose a novel cross-domain code vulnerability detection framework named MNCRI. Specifically, we introduce mutual nearest neighbor contrastive learning to align the source domain and target domain geometrically, which could align the common semantic characteristics of two domains and separate out the private semantic characteristics of each domain. Furthermore, we introduce an instance re-weighting scheme to alleviate the problem of excessive alignment. This scheme dynamically assign different weights to instances, reducing the contribution of irrelevant instances so as to achieve better domain alignment. Finally, extensive experiments demonstrate that MNCRI significantly outperforms state-of-the-art cross-domain code vulnerability detection methods by a large margin.