Weir was handed his first management job at Bramall Lane in the summer, but his brief reign was cut short after only a handful of games, with the club third from bottom in League One.
Tuesday's defeat by Hartlepool in the Johnstone's Paint Trophy prompted the board to take action and Chris Morgan takes charge as caretaker manager for the trip to Coventry on Sundays.
The Blades were expected to challenge for promotion this season, but have failed to pick up a victory since the opening day.
Assistant manager Lee Carsley joined Weir in being told to leave United.
Chief executive Julian Winter said: "First and foremost all at SUFC, from the board right the way through the club, wish David and Lee all the best for the future. None of us wanted to be in this position at this point in the season. David's appointment was made as part of developing a new phase at the club.
"Chris Morgan has been asked and agreed to take an interim role in charge of Sunday's team. He knows the players and, with Darren and Travis, will be doing his upmost to get a return to winning ways."
Morgan said: "The club have made me aware of the situation and I am happy to step in and work with the players for the Coventry game."
Morgan, a long-serving former defender with United, had a spell as caretaker boss last season following the departure of Danny Wilson and was working as a coach under Weir.
Weir was chosen eventually as the permanent replacement for Wilson but lost nine of United's 13 matches in all competitions.
Saudi Arabian Prince Abdullah bin Mosaad purchased 50 per cent of the club's share from owner and chairman Kevin McCabe last month and gave Weir his full backing.
But the club's fans have consistently expressed their concern at such a poor start to their third season in the third tier, which has seen the Blades lose five of their last six games.