The class imbalance problem arises in the current end-to-end models for the emotion-cause pair extraction (ECPE) task, and a large number of negative clause pairs interfere model to depict the characteristics of emotion and cause. Most existing methods adopt a window-constrained strategy to limit the relative distance between candidate clauses to a smaller range to filter negative pairs. However, those methods ignore the semantic association between distant clauses, and using an artificial window size is imperfect due to the inherent ambiguity and delicacy of emotion. Inspired by the centrality principle of discourse, in this paper we propose a select-then-extract framework for the ECPE task, where the core clauses are first selected from the original document as candidate emotion and cause clauses, and then emotions, causes and emotion-cause pairs are jointly extracted from the candidate clauses. Specifically, our model includes two main components: core clause selector and emotion-cause pairs extractor. For the Core Clause Selector, we introduce the extractive document summarization (EDS) task and present a multi-granularity semantic awareness cooperative graph model (MGCOG) to extract core clauses from documents. Compared to the previous methods, the core clause selector is more effective for alleviating the category imbalance because the global causal cues and context can be captured by learning global keywords and inter-clause relationships, which determines more efficient candidate clauses. For Emotion-Cause Pairs Extractor, we put forward a multi-task learning model to jointly extract emotions, causes and emotion-cause pairs from the selected core clauses. Here, a multi-head attention is used to further model the relationship between candidate clauses, and a co-predictor is designed for assigning scores to all possible emotion-cause pairs. We further investigate the pipeline and the joint model under the select-then-extract framework, and show that the experimental results on benchmark datasets are consistently superior to the comparative baseline models. Extensive ablation experiments also verify the effectiveness of each component.