Space-air-ground-sea integrated network (SAGSIN), which integrates satellite communication networks, aerial networks, terrestrial networks, and marine communication networks, has been widely envisioned as a promising network architecture for 6G. In consideration of its cooperation characteristics of multi-layer networks, open communication environment, and time-varying topologies, SAGSIN faces many unprecedented security challenges, and there have been a number of researches related to SAGSIN security performed over the past few years. Based on such observation, we provide in this paper a detailed survey of recent progress and ongoing research works on SAGSIN security in the aspects of security threats, attack methodologies, and defense countermeasures. To the best of our knowledge, we are the first to present the state-of-the-art of security for SAGSIN, since existing surveys focused either on a certain segment or on several segments of the integrated network, and little can be found on the full coverage network. In addition to reviewing existing works on SAGSIN security, we also present some discussions on cross-layer attacks and security countermeasure in SAGSIN, and identify new challenges ahead and future research directions.