Colonoscopy is considered the best diagnostic tool for early detection and resection of polyps, which can effectively prevent consequential colorectal cancer. In clinical practice, segmenting and classifying polyps from colonoscopic images have a great significance since they provide precious information for diagnosis and treatment. In this study, we propose an efficient multi-task synergetic network (EMTS-Net) for concurrent polyp segmentation and classification, and we introduce a polyp classification benchmark for exploring the potential correlations of the above-mentioned two tasks. This framework is composed of an enhanced multi-scale network (EMS-Net) for coarse-grained polyp segmentation, an EMTS-Net (Class) for accurate polyp classification, and an EMTS-Net (Seg) for fine-grained polyp segmentation. Specifically, we first obtain coarse segmentation masks by using EMS-Net. Then, we concatenate these rough masks with colonoscopic images to assist EMTS-Net (Class) in locating and classifying polyps precisely. To further enhance the segmentation performance of polyps, we propose a random multi-scale (RMS) training strategy to eliminate the interference caused by redundant information. In addition, we design an offline dynamic class activation mapping (OFLD CAM) generated by the combined effect of EMTS-Net (Class) and RMS strategy, which optimizes bottlenecks between multi-task networks efficiently and elegantly and helps EMTS-Net (Seg) to perform more accurate polyp segmentation. We evaluate the proposed EMTS-Net on the polyp segmentation and classification benchmarks, and it achieves an average mDice of 0.864 in polyp segmentation and an average AUC of 0.913 with an average accuracy of 0.924 in polyp classification. Quantitative and qualitative evaluations on the polyp segmentation and classification benchmarks demonstrate that our EMTS-Net achieves the best performance and outperforms previous state-of-the-art methods in terms of both efficiency and generalization.