The 51-year-old, whose contract was due to expire at the end of the season, leaves the club after guiding the team to just two wins in seven matches of the Super League season.
As it stands, the Giants, who finished inside the top eight last season, are second from bottom in the table.
Managing director Richard Thewlis said in a statement: "It is a very difficult call for any club to make in respect of the head coach but the board felt that a change was needed and that the change should be made sooner rather than later with much of the season still to run.
"Rick Stone is an outstanding man, character and coach but the results for us simply haven't worked out as anyone would have wished for."
Stone's assistant Chris Thorman has been given the reins.