MD-11 Captain reported encountering wake turbulence from a preceding B777 on descent into MEM that resulted in an inflight upset. Control was regained and the flight landed safely.

Narrative

While on the BLUZZ 5 arrival into MEM; we experienced three separate wake turbulence events behind a B777 resulting in up to 40 degrees of uncommanded roll and causing our Autopilot to disconnect on two of those events. During the second event we were cleared to descend to and maintain 10;000 feet. At approximately 10;500 feet; we experienced the uncommanded roll and subsequent Autopilot uncommanded disconnect and while the pilot flying (PF) was regaining positive aircraft control; we descended to 9;700 ft and advised ATC that were in severe wake turbulence and descended to 9700ft and were climbing back to 10;000 ft. ATC told us not to climb back up and to continue our descent to a lower altitude (I forgot the exact cleared altitude). At this point we asked to be vectored off the STAR for the remainder of the arrival and approach into MEM.Cause: We did not have sufficient separation from the preceding B777 on the arrival given the winds.Suggestions: Increased separation behind heavier aircraft on the arrival. Better analysis on my part of the given winds and lack of sufficient separation on the arrival.