In Software-Defined Networking (SDN)-enabled cloud data centers, live migration is a key approach used for the reallocation of Virtual Machines (VMs) in cloud services and Virtual Network Functions (VNFs) in Service Function Chaining (SFC). Using live migration methods, cloud providers can address their dynamic resource management and fault tolerance objectives without interrupting the service of users. However, in cloud data centers, performing multiple live migrations in arbitrary order can lead to service degradation. Therefore, efficient migration planning is essential to reduce the impact of live migration overheads. In addition, to prevent Quality of Service (QoS) degradations and Service Level Agreement (SLA) violations, it is necessary to set priorities for different live migration requests with various urgency. In this paper, we propose SLAMIG, a set of algorithms that composes the deadline-aware multiple migration grouping algorithm and on-line migration scheduling to determine the sequence of VM/VNF migrations. The experimental results show that our approach with reasonable algorithm runtime can efficiently reduce the number of deadline misses and has a good migration performance compared with the one-by-one scheduling and two state-of-the-art algorithms in terms of total migration time, average execution time, downtime, and transferred data. We also evaluate and analyze the impact of multiple migration planning and scheduling on QoS and energy consumption.