Cross-domain named entity recognition aims to improve performance in a target domain with shared knowledge from a well-studied source domain. The previous sequence-labeling based method focuses on promoting model parameter sharing among domains. However, such a paradigm essentially ignores the domain-specific information and suffers from entity type conflicts. To address these issues, we propose a novel machine reading comprehension based framework, named DoSEA, which can identify domain-specific semantic differences and mitigate the subtype conflicts between domains. Concretely, we introduce an entity existence discrimination task and an entity-aware training setting, to recognize inconsistent entity annotations in the source domain and bring additional reference to better share information across domains. Experiments on six datasets prove the effectiveness of our DoSEA. Our source code can be obtained from https://github.com/mhtang1995/DoSEA.