The others who were terminated included bench coach Ramon Vazquez, hitting coach Peter Fatse, third base coach Kyle Hudson, assistant hitting coach Dillon Lawson, and hitting strategy coach Joe Cronin.
Chad Tracy, manager of Boston's Triple-A affiliate team, the Worcester Red Sox, was named as the interim manager.
The move came after the Red Sox teed off on the Baltimore Orioles in a 17-1 win.
However, Cora, who led Boston to glory in his debut season in 2018, departs with the Red Sox in last place in the American League East division with a 10-17 record.
Since Cora's victorious first season, the Red Sox - one of Major League Baseball's most decorated sides - have only reached the postseason on two occasions.
"Alex Cora led this organization to one of the greatest seasons in Red Sox history in 2018, and for that, and the many years that followed, he will always have our deepest gratitude," said Red Sox principal owner John Henry.
"He has had a lasting impact on this team and on this city. He has led on and off the field in so many important ways."
"These decisions are never easy, but this one is especially difficult given what Alex has meant to the Red Sox since the day he arrived."
Cora, 50, is the first Puerto Rican coach to win a World Series.
His tenure as Red Sox manager consisted of two stints.
He parted ways with Boston in January 2020 following his implication in a sign-sealing scandal during his previous role as Houston Astros bench coach.
Houston had used illicit technology, including a video camera to pick up opposing catchers' signs to pitchers about what sort of ball would be thrown next to Astros batters.
Cora was re-hired by Boston when his MLB suspension ended in November 2020. The Red Sox then reached the American League Championship Series in 2021.