The former Leicester Tigers fly-half, 29, took over in August, returning to Emerald Headingley for the fourth time in his career.
Along with director of rugby Martyn Wood, he helped completely rebuild the squad after it was decimated by a CVA and played a crucial part on and off the field at the height of their troubled times.
However, with the club still awaiting a first win, Wood was sacked just before Christmas as Phil Davies was lined up to return to take up the reins in the new year.
Ex-Northampton Saints and Sale Sharks No10 Ford played in Davies’ first game in charge - a 52-0 loss at Cornish Pirates - but was absent in the following defeat against Championship leaders Newcastle Falcons on Sunday due to ‘illness.’
As they remain in the relegation dogfight, Davies has turned to his former Wales team-mate Colin Stephens to try and help claw them clear of the botton of the table.
“It is disappointing to be losing Joe as I was looking forward to working with him as a young, English coach who knew the club, having come through the academy,” he said.
“I fully understand the demands of juggling his new business with his rugby commitments and he leaves with our best wishes.”
Stephens, the 50-year-old former fly-half who made four Test appearances, was a team-mate of Davies’ at Llanelli, Leeds Tykes and Wales.
He has been based in Leeds since initially moving to the club in 1995, including roles as Morey player-coach, and is currently director of rugby at Leeds Beckett University who sit top of the BUCS Super Rugby table.
Stephens, who will work part-time, helped assist Davies against Newcastle and will also join up for tomorrow night’s game at Jersey.
Davies has also recruited another former Wales team-mate Wayne Proctor, who worked with him for Namibia at last year’s World Cup, on a consultancy basis as head of strength and conditioning.
Carnegie managing director Chris Gibson added: “On behalf of everyone at the club, I would like to thank Joe for his efforts for the club during a difficult period.
“Before appointing Phil Davies, we were looking to bring in Colin Stephens to give support to Joe as a young Head Coach but we understand the reasons for his decision and wish him all the best for the future.”