McDonough said he, interim coach Jay Triano and Bledsoe met Monday morning and that Bledsoe was sent home at the end of the discussion. He will not play in Monday's home game against the Sacramento Kings.
Bledsoe "won't be with us going forward," McDonough said.
McDonough said he called Bledsoe on the phone to inquire about the veteran guard's tweet Sunday, when he posted "I Don't wanna be here" hours before the Suns fired Earl Watson.
"He said he was at a hair salon," McDonough told reporters. "It wasn't about the Suns or anything related to the Suns. He said he was at a hair salon with his girl and that he didn't wanna be there anymore.
"I don't believe that to be true. We thought about it and talked about it with [owner] Robert [Sarver] and my staff and Coach Triano and his staff and decided it's what's best for the organization."
McDonough said he already has received calls from teams about Bledsoe's availability and that he planned to answer them.
The general manager is actively engaged with several teams in trade talks for Bledsoe, league sources told ESPN's Adrian Wojnarowski, and the team hopes to make a deal soon.
Interest around the NBA has increased in the past day for Bledsoe once it became apparent that both sides were motivated to part ways, sources told Wojnarowski.
League sources told ESPN's Ian Begley that the New York Knicks are among the teams that have reached out about a possible Bledsoe trade.
In the preseason, Bledsoe arranged a meeting with Sarver and McDonough and requested a trade, league sources told ESPN.
Sources said Bledsoe has voiced his frustration with the direction of the team. He covets to be in a winning situation. The organization, sources said, argues that the team hasn't improved since Bledsoe took over the bulk of the playmaking duties.
Bledsoe is the Suns' highest-paid player this season, making $14.5 million. He is owed $15 million for 2018-19, the final year of his contract. He is averaging 15.7 points and three assists per game for the Suns this season. He has career averages of 13.1 points, 3.8 rebounds and 4.6 assists per game.
The Suns lost 130-88 on Saturday night to the LA Clippers, dropping Phoenix to 0-3. The franchise's opening night 124-76 loss to the Portland Trail Blazers was the biggest blowout loss in Suns history.
McDonough also said Monday that his relationship with Watson "wasn't great" and that it was "time for a new voice, a new direction." He said the ugly losses weren't the sole reason for the firing.
"We had a number of meetings over the summer about some of the changes we would have liked to see in terms of style of play and player development and accountability," McDonough said, "all those things that go into winning and helping players develop and improve. Unfortunately, we didn't see those changes."
McDonough said Triano would be head coach the remainder of the season. Triano described himself as a basketball guy and said he didn't know whether he wanted the job beyond this season.
"We'll see how it goes," Triano said, "but I'm going to embrace it 100 percent and dive into it like I have everything else in my career."
McDonough, who said he recommended the firing to Sarver, accepted some responsibility for the team's troubles.
"I think we all do," McDonough said. "I think Robert does. I think I do. It reflects poorly on all of us and we own that and we take responsibility for that."
A strong supporter of Watson, guard Devin Booker said the players are responsible for the awful performances.
"You can't blame two 40-point losses on a coach," Booker said. "That comes with pride. It comes with effort and love for the game. We haven't shown that yet."
The Associated Press contributed to this report.