Sharks coach, Chris Lynch, said: "Basketball players do come back from this injury. But they're the guys earning eight million dollars a year who are prepared to trade off the pain for the cash. I am not sure that Matt, at 25, can put himself through all that again just to get back to ground zero, which is where he was before it happened on Sunday."
Gaudio was rebuilding his career with the Sharks after suffering the previous injury playing in Italy. He had been a major factor in Sheffield's 12-game unbeaten start to the season, averaging 15 points and seven rebounds.
He was injured early in the second quarter of their 87-85 defeat at Derby Storm.
Finch said: "Matt made a jump stop, tried to change direction and his knee went. We've asked him to stay on as an assistant coach, but he is going back to the US to start his life over."
The Sharks are signing Peter Scantlebury, England's most capped player. He should make his debut on Sunday.