Corporate G650 Captain reported encountering wake turbulence descending into LAS in trail of a B777 that resulted in speed and altitude deviations.

Narrative

While attempting to expedite our descent (at ATC request) into LAS; we encountered wake turbulence in the trail of a Boeing 777. This led to a roll right and left each of 40 degrees and a loss of altitude of about 250 feet. After correcting; we requested a deviation away from traffic to left-offset the 777's flight path. We were granted some relief; but soon found ourselves back in trail as we entered the CHOWW TWO STAR. Due to this; when we first started on the CHOWW 2; we needed more clarity about our assigned altitude. The Controller instructed us initially to level off to allow the 777 to get below us but then promptly assigned us a descend 'via.' This initially led to us being off course and high at the beginning of the STAR. Compounding this was the request from ATC to declare any injuries or damage to our aircraft and; finally; another Controller handoff.One of the final Controllers estimated that we would not be able to reach our next assigned altitude as we approached TATUU on the CHOWW 2. When we attempted to expedite our descent to comply; we pushed the nose too far over and attained a speed of 264 knots in a 250 knot restricted airspace. We never entirely made it to the point in question (TATUU) as we were vectored off the STAR by ATC. We were then advised of possible pilot deviation and given a number to call.Where I screwed up: Following the wake turbulence event; I acknowledge that we should have IMMEDIATELY requested vectors away from the STAR and sought ATC assistance. It shook us up; and we were overwhelmed by continual turbulence as we stayed behind the 777 down the chute. It compounded our already heavy workload; and we were reluctant to descend into the wake turbulence again for fear of injury or damage to our aircraft.