Software-defined satellite network (SDSN) is a novel framework, which brings softwaredefined network technologies in the satellite networks. It has great potential to achieve effective and flexible management in the satellite networks. There are two burning issues to be solved for the flow table management in SDSN. First, the ternary content addressable memory (TCAM) space is limited on satellites and the flow table size should be reduced. Second, the frequent handovers will lead to an increase in the flow table size in SDSN. Due to the limited flow table space, a lot of flows will be dropped if the flow table is full during the handover. To address these issues, we first give a description of our focused flow table management problems. Then, we propose SAT-FLOW, a multi-strategy flow table management method for SDSN. SAT-FLOW considers three key points, limited TCAM space, classified traffic, and handover. SAT-FLOW contains two heuristic algorithms, named dynamic classified timeout (DCT) algorithm and timeout strategybased mobility management (TSMM) algorithm. DCT aims to reduce the flow table size and TSMM aims to reduce the drop flows during the handover. We implement SAT-FLOW and conduct contrast experiments. The experimental results verify the good performance in terms of transmission quality, idle_timeout values distribution, a 15.27%-24.34% decrease in flow table size, an 8.2%-10.4% decrease in drop-flow rate, and a 4.92%-5.7% decrease in table misses for the high priority traffic during the handover.