The zombie drama was picked up for a fourth season in December without showrunner Mazzara, with reports later emerging that he had been fired following a series of creative disagreements.
"We love the show, and we admire and cherish the work of everybody involved who made it an extraordinarily well-crafted TV series," Sapan told The Hollywood Reporter.
"In the case of Glen, we decided mutually to part ways."
Sapan claimed that, despite Mazzara's departure, his network continues to hold "people who make great TV shows... in extraordinarily high regard".
"Certainly it would be preferable to have as much continuity as possible," he conceded. "[But] we'll forge ahead and hope to make great shows and be the best place to work."
Scott Gimple (FlashForward, Life) will assume the role of showrunner on The Walking Dead at the beginning of the show's fourth season.
The second half of season three - Mazzara's final episodes - will air in the US from Sunday, February 10 and on FOX in the UK from Friday, February 15.
> Kurt Sutter slams AMC for Glen Mazzara 'Walking Dead' exit
Watch a promo for The Walking Dead below: