Cora served as manager A.J. Hinch's bench coach during the season in which the Astros were found to be using technology to steal opposing pitchers' signs.
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"Today we met to discuss the Commissioner's report related to the Houston Astros investigation. Given the findings and the Commissioner's ruling, we collectively decided that it would not be possible for Alex to effectively lead the club going forward and we mutually agreed to part ways," the Red Sox said in a statement.
"I do not want to be a distraction to the Red Sox as they move forward," added Cora, who managed Boston to the 2018 World Series title.
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Similar to Houston's, Boston's championship season during Cora's first season with the Red Sox is also being investigated by Major League Baseball. MLB stated Cora's possible punishment related to the Astros will be known after the completion of the Red Sox probe.
A day earlier, MLB suspended Hinch and general manager Jeff Luhnow for a year. They were then immediately fired by the Astros.