Cross-domain recommendation (CDR) aims to enhance the recommendation accuracy in a target domain with sparse data by leveraging rich information in a source domain, thereby addressing the data-sparsity problem. Some existing CDR methods highlight the advantages of extracting domain-common and domain-specific features to learn comprehensive user and item representations. However, these methods cannot effectively disentangle these components, as they often rely on simple user-item historical interaction information (such as ratings, clicks, and browsing), neglecting the rich multi-modal features. In addition, they do not protect user-sensitive data from potential leakage during knowledge transfer between domains. To address these challenges, we propose a Privacy-Preserving Framework with Multi-Modal Data for Cross-Domain Recommendation, called P2M2-CDR. Specifically, we first design a multi-modal disentangled encoder that utilizes multi-modal information to disentangle more informative domain-common and domain-specific embeddings. Furthermore, we introduce a privacy-preserving decoder to mitigate user privacy leakage during knowledge transfer. Local differential privacy (LDP) is used to obfuscate disentangled embeddings before the inter-domain exchange, thereby enhancing privacy protection. To ensure both consistency and differentiation among these obfuscated disentangled embeddings, we incorporate contrastive learning-based domain-inter and domain-intra losses. Extensive experiments conducted on six CDR tasks from two real-world datasets demonstrate that P2M2-CDR outperforms other state-of-the-art single- and cross-domain baselines. The code is available at https://github.com/Lili1013/P2M2-CDR.