Matt Prestridge, coach and head of sports science, goalkeeping coach Darren Ward and analyst Mike Allen have departed by mutual consent.
The news was confirmed in a short statement on United's official website.
"The trio, members the backroom staff for a number of years, leave Bramall Lane with immediate effect," it continued.
"The Board thank them for their hard work and wish them well for the future."
Prestridge worked with Wilder and his assistant Alan Knill, whose future is unclear after he was offered a de facto director of football role at Bramall Lane, in their previous job at Northampton Town.
Formerly of clubs such as Watford, Derby and Spurs, Prestridge was also a member of Wilder’s brains trust at Bramall Lane.
Ward, who was already at Bramall Lane when Wilder arrived, was hailed by Dean Henderson as the best goalkeeping coach he had ever worked with during his loan spell at Bramall Lane.
“Wardy has been outstanding,” Henderson said in 2019 after his first season on loan at Bramall Lane, as quoted in the Blades promotion book We’re not going to Wembley.
“The best goalkeeping coach I've ever worked with. He's brought me on leaps and bounds in every aspect of the game - mentally, physically, tactically - and the sessions are brilliant.
“I look forward to coming into work every day, and long may that continue. If I could work with Wardy for the next couple of years, I really think I can elevate to one of the best goalkeepers in the world.”