Space-air-ground integrated networks (SAGIN) provide great strengths in extending the capability of ground wireless networks. On the other hand, with rich spectrum and computing resources, the ground networks can also assist space-air networks to accomplish resource-intensive or power-hungry missions, enhancing the capability and sustainability of the space-air networks. Therefore, bi-directional mission offloading can make full use of the advantages of SAGIN and benefits both space-air and ground networks. In this article, we identify the key role of network reconfiguration in coordinating heterogeneous resources in SAGIN, and study how network function virtualization (NFV) and service function chaining (SFC) enable agile mission offloading. A case study validates the performance gain brought by bi-directional mission offloading. Future research issues are outlooked as the bi-directional mission offloading framework opens a new trail in releasing the full potentials of SAGIN.