Murray, 53, was hired Jan. 9, 2014, after eight seasons as an assistant GM with the Ottawa Senators. Among his moves were hiring Bylsma, selecting forward Jack Eichel with the No. 2 pick in the 2015 NHL Draft, and acquiring forward Evander Kane and defenseman Zach Bogosian in a trade with the Winnipeg Jets on Feb. 11, 2015.
Murray, whose original contract with Buffalo ran through this season, signed a multiyear extension in October before the Sabres' first game.
The firings come a day after a Buffalo radio station reported that Eichel told the Sabres he had no desire to sign a contract extension if Bylsma remained coach.
Eichel denied that report, telling The Buffalo News his end-of-season interviews with Bylsma and Murray went well and that he wants to stay with Sabres long term. The 20-year-old center is entering the final year of his three-year entry-level contract and can sign an extension beginning July 1. He could become a restricted free agent following next season.
"I want to be here for a long time," Eichel said Wednesday. "That's the way I look at it. I don't want to go anywhere else. I don't want anybody to think that I want to be somewhere else. ... I want to be a Sabre and I want to be a Sabre for a long time and I want to be a part of Buffalo when we win. I know it's an organization that is capable of doing that, and I want to be a part of it and I want to be a centerpiece of it.
"Just hearing these things that people are writing after I have a meeting with Tim and a meeting with Dan, I thought both of them went well. None of anything that I've read so far has been accurate of what was said in those meetings with them. It's a bit frustrating and a bit disheartening because I thought things were heading in the right direction leaving Buffalo. As much as we didn't have a great year, you've got to just look forward to the future."
Murray, who replaced Darcy Regier as GM, said after the season he would attempt to start negotiations with Eichel for a contract extension as soon as he was allowed to.