Accurate segmentation of the polyps from colonoscopy images provides useful information for the diagnosis and treatment of colorectal cancer. Despite deep learning methods advance automatic polyp segmentation, their performance often degrades when applied to new data acquired from different scanners or sequences (target domain). As manual annotation is tedious and labor-intensive for new target domain, leveraging knowledge learned from the labeled source domain to promote the performance in the unlabeled target domain is highly demanded. In this work, we propose a mutual-prototype adaptation network to eliminate domain shifts in multi-centers and multi-devices colonoscopy images. We first devise a mutual-prototype alignment (MPA) module with the prototype relation function to refine features through self-domain and cross-domain information in a coarse-to-fine process. Then two auxiliary modules: progressive self-training (PST) and disentangled reconstruction (DR) are proposed to improve the segmentation performance. The PST module selects reliable pseudo labels through a novel uncertainty guided self-training loss to obtain accurate prototypes in the target domain. The DR module reconstructs original images jointly utilizing prediction results and private prototypes to maintain semantic consistency and provide complement supervision information. We extensively evaluate the proposed model in polyp segmentation performance on three conventional colonoscopy datasets: CVC-DB, Kvasir-SEG, and ETIS-Larib. The comprehensive experimental results demonstrate that the proposed model outperforms state-of-the-art methods.