Cross-domain Recommendation (CDR) aims to alleviate the data sparsity and the cold-start problems in traditional recommender systems by leveraging knowledge from an informative source domain. However, previously proposed CDR models pursue an imprudent assumption that the entire information from the source domain is equally contributed to the target domain, neglecting the evil part that is completely irrelevant to users' intrinsic interest. To address this concern, in this paper, we propose a novel knowledge enhanced cross-domain recommendation framework named CoTrans, which remolds the core procedures of CDR models with: Compression on the knowledge from the source domain and Transfer of the purity to the target domain. Specifically, following the theory of Graph Information Bottleneck, CoTrans first compresses the source behaviors with the perception of information from the target domain. Then to preserve all the important information for the CDR task, the feedback signals from both domains are utilized to promote the effectiveness of the transfer procedure. Additionally, a knowledge-enhanced encoder is employed to narrow gaps caused by the non-overlapped items across separate domains. Comprehensive experiments on three widely used cross-domain datasets demonstrate that CoTrans significantly outperforms both single-domain and state-of-the-art cross-domain recommendation approaches.