Service migration is crucial in mobile edge computing (MEC) to ensure seamless service provision as users move. Although some migration schemes have been proposed, they fail to efficiently support the migration of microservices in a directed acyclic graph (DAG)-based service across different edge servers, resulting in high service latency. This paper focuses on the DAG-based service migration problem and proposes a collaborative microservice migration framework for MEC, aiming to minimize the service migration latency while efficiently distributing the migration workload across edge servers. We divide edge servers into clusters and formulate the DAG-based service migration problem as a two-stage optimization problem. In the first stage, a deep reinforcement learning-based service pre-migration algorithm is developed to identify the optimal cluster of edge servers for hosting the migrated service. In the second stage, a microservice migration algorithm is devised, utilizing topological sorting and network flow techniques to further determine the target edge server for each microservice. Our design addresses the inherent dependencies among microservices within a DAG task and adapts well to dynamic network environments. Experimental results on real-world datasets demonstrate that our approach significantly reduces service migration latency.