No replacement was named; the Sharks also fired assistants John Madden, John MacLean and Dan Darrow.
Boughner was 67-85-23 in three seasons with San Jose. He became coach Dec. 11, 2020, when he was promoted from an assistant role to replace the fired Peter DeBoer.
"Up until yesterday, they were our coaching staff," Sharks assistant general manager Joe Will said. "There were lots of things they could hang their hat on. But as we go further into this review, and it's been very thorough in a lot of different areas, we just came to the conclusion that amongst everything else, we just want this fresh start moving forward with a general manager and a head coach.
"It's not solely on the coaches for the performance from the past season. It's a shared thing between myself and our management team, and the coaches and the players. We all need to get better."
The Sharks went 32-37-13 this season, finishing 20 points behind the Nashville Predators for the second wild card into the Stanley Cup Playoffs from the Western Conference. It was the third straight season they failed to qualify for the postseason after reaching the playoffs 14 of the previous 15 seasons.
"As we progress through our search for the next general manager of the Sharks following 19 seasons under (former general manager) Doug Wilson's leadership, it has become apparent that the organization is in the process of an evolution," Will said. "... As part of this evolution and evaluation, we felt it was in the best interest of the club to allow the next Sharks general manager to have full autonomy related to the make-up of the on-ice coaching staff moving ahead."
Prior to his time in San Jose, Boughner coached the Florida Panthers from 2017-19, going 80-62-22 in two seasons before he was fired after the 2018-19 season and replaced by Joel Quenneville.
The 51-year-old is 147-147-45 as an NHL coach with no appearances in the postseason.
When Wilson stepped down as GM on April 7 after 19 seasons with the Sharks, owner Hasso Plattner said Will, who was GM during Wilson's medical leave, would continue in that role while the team conducts a search among external candidates. The search committee includes Plattner, Will and Sharks president Jonathan Becher.
With the Winnipeg Jets hiring Rick Bowness on Sunday, the Sharks are the only NHL team sitll searching for a coach.
"There's going to be plenty of quality candidates," Will said.
NHL.com independent correspondent Chelena Goldman contributed to this report
