The Bucks looked poised to claim only their second win of the season after a 41-point performance from Damian Lillard, who gave his side a 113-112 lead after draining a jumper with 10 seconds left on the clock.
But Mitchell expertly ran the final few seconds down before nervelessly sinking the final bucket to leave Milwaukee's Fiserv Forum in stunned silence.
There was still time for one last attempted buzzer-beater from Lillard, but the Bucks' star's effort bounced off the backboard to leave Cleveland sitting pretty with a perfect 7-0 record on top of the Eastern Conference.
Mitchell, who finished with 30 points, four assists and three rebounds, credited his game-winning shot to a possession-securing rebound by team-mate Isaac Okoro moments before.
"It's not about the shot -- it's about Isaac Okoro's rebound," Mitchell said. "That's what it's all about. I did my job, Isaac did his job, we all did our jobs.
"That's a big win. They played their behinds off. As a group we just continue to fight and claw."
The all-round performance saw six Cavaliers players make double figures in a see-saw clash that included 19 lead changes.
Sam Merrill caught the eye with 17 points off the bench for Cleveland, raining in five three-pointers while Jarrett Allen had 15 points with 12 rebounds.
The Bucks were left pondering another uneven performance which has left them one place off the bottom of the Eastern Conference with a 1-5 record.
Lillard, who scored just four points in a blowout defeat to Memphis on Thursday, bounced back in scintillating fashion, shooting 10-of-15 from outside the arc for the Bucks.
Giannis Antetokounmpo also impressed in Milwaukee's losing effort, finishing with 34 points and 16 rebounds.
Thunder roll on
In other games Saturday, the Oklahoma City Thunder remain the only other unbeaten team in the league after recovering from a 13-point first-half deficit to defeat the Los Angeles Clippers 105-92.
Shai Gilgeous-Alexander led Oklahoma City with 25 points as the Thunder improved to 5-0 to remain in top spot in the Western Conference.
The Phoenix Suns remain in second place in the West on 5-1 after scoring a 103-97 defeat of the Portland Trail Blazers.
In Denver, the Nuggets improved to 3-3 for the season with a 129-103 blowout of the Utah Jazz, with Nikola Jokic just missing out on a triple double after finishing with 27 points, 16 rebounds and nine assists.
In Charlotte, Jayson Tatum's 29 points helped NBA champions Boston down the Hornets for a second straight night, the Celtics winning 113-103 at the Spectrum Center in Charlotte.
Payton Pritchard again shone off the bench for Boston, delivering six three-pointers in a 22-point cameo. Luke Kornet added 19 points with Derrick White finishing with 18.
Tatum's performance in the face of stifling defensive pressure from Charlotte earned praise from Boston coach Joe Mazzulla.
"They doubled him and he made the right play every time," Mazzulla said of Tatum. "I think he played a great game.
"I thought he had tremendous poise throughout the game and understanding of how the defense was guarding him."
In Philadelphia, the 76ers' rocky start to the season continued in the absence of injured duo Joel Embiid and Paul George, with Memphis powering to a 123-107 win.
Jaren Jackson Jr. led the Grizzlies with 27 points, with Ja Morant adding 18 points and 12 assists as Memphis improved to 4-3.
The NBA said after the game it was investigating reports that Embiid was involved in a locker-room altercation with a journalist following the defeat.
"We are aware of reports of an incident in the Sixers locker room this evening and are commencing an investigation," an NBA spokesman was quoted by US media as saying.
The San Antonio Spurs improved to 3-3 with a 113-103 defeat of the Minnesota Timberwolves while the in-form Golden State Warriors moved to 5-1 with a 127-121 defeat of the Houston Rockets.
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