Event coreference resolution aims to classify all event mentions that refer to the same real-world event into the same group, which is necessary to information aggregation and many downstream applications. To resolve event coreference, existing methods usually calculate the similarities between event mentions and between specific kinds of event arguments. However, they fail to accurately identify paraphrase relations between events and may suffer from error propagation while extracting event components (i.e., event mentions and their arguments). Therefore, we propose a new model based on Event-specific Paraphrases and Argument-aware Semantic Embeddings, thus called EPASE, for event coreference resolution. EPASE recognizes deep paraphrase relations in an event-specific context of sentences and can cover event paraphrases of more situations, bringing about a better generalization. Additionally, the embeddings of argument roles are encoded into event embedding without relying on a fixed number and type of arguments, which results in the better scalability of EPASE. Experiments on both within- and cross-document event coreference demonstrate its consistent and significant superiority compared to existing methods.