"After reviewing the past season and looking at the future of our organization, Kim and I have chose to relieve General Manager Tim Murray and Head Coach Dan Bylsma of their duties".
Last week, Murray had backed Bylsma returning for a third season as coach.
Murray hinted last week that his future in Buffalo, and that of Bylsma, were uncertain.
The Sabres found themselves in the basement of the Atlantic Division in 2016-17 after posting a 33-37-12 mark.
Bylsma, who led the Pittsburgh Penguins to a Stanley Cup title in 2009, had a 68-73-23 record in his two seasons with the Sabres.
Owner Terry Pegula made the announcement after he spent the past two days holding season-ending meetings with Murray.
Pegula's frustrations in the Sabres go even deeper after he vowed to build the team into a victor upon purchasing the franchise in February 2011. The Sabres finished last overall in 2014-15 and received the best odds of winning the draft lottery, but they lost out to Edmonton and chose Eichel with the second overall pick. Injuries played a role in this season's collapse, with Eichel missing the first 21 games because of a sprained left ankle. Bylsma took the helm the next year, replacing Ted Nolan.
Murray, 53, joined the Sabres as their GM in 2014.
"It needs fixing", Murray said. "And I personally have to make more demands of myself".