In the field of heterogeneous remote sensing image change detection, particularly in natural disaster assessment, the fusion of optical and synthetic aperture radar (SAR) images is widely applied. However, due to differences in resolution and imaging mechanisms of heterogeneous remote sensing data, existing deep learning methods often lose original image features and introduce additional noise, leading to suboptimal detection results. To resolve these challenges, this study introduces a Mamba-based Siamese Network (Mamba-OSCDNet) that combines cross-attention fusion with contrastive learning. The network introduces a Cross-Attention-based Mamba Fusion Mechanism (CAMFM), which effectively enhances the feature interaction and channel information between heterogeneous images. In addition, to alleviate the category imbalance problem, this paper adopts a contrastive learning strategy and designs a weighted composite loss function, which significantly reduces the leakage detection rate. The findings show that the new method outperforms current techniques on various benchmark datasets. Taking the Gloucester I dataset as an example, the method attains an F1 score of 95.11% and an overall accuracy of 99.37%, representing improvements of 7.75% and 1.08%, respectively, over the best-performing baseline.