"I am sorry that Bryan and Don have decided to resign their spots, but I wish them nothing, but the best in their future," manager Mike Hargrove said Monday.
The 56-year-old Baylor, former manager of the Colorado Rockies and the Chicago Cubs, spent one season as Hargrove's hitting coach. Price spent the past six seasons as the Mariners' pitching coach under managers Lou Piniella, Bob Melvin and Hargrove. Price, 43, worked 18 seasons in the Seattle organization.
The Mariners were last in the AL West at 69-93 in their first year under Hargrove, an improvement of six wins from 2004.
Despite the free-agent additions of Adrian Beltre and Richie Sexson, the Mariners hit an AL-low .256 with 130 homers and 699 runs.
"I have decided not to return as hitting coach so that I will be able to pursue other opportunities," said Baylor, who managed the Rockies from 1993-1998 and the Cubs from 2000-2002.
Seattle's starting pitchers had a 50-64 record and a 4.91 ERA, but the team's bullpen was a surprise with a 19-29 record and a 3.60 ERA. Under Price, Mariners pitchers ranked among the major league leaders in four of six seasons.
"I have enjoyed my time here but, after 18 years, I think it is time for me to go somewhere else," Price said. "For me to keep growing as a coach, I need to get out of my comfort zone and this is a way to do that."
Third base coach Carlos Garcia, interim first base coach Mike Goff, bench coach Ron Hassey and bullpen coach Jim Slaton have been invited to return to Hargrove's coaching staff next season. The team said Jeff Newman, who started the season as third base coach before an Achilles' injury, won't return.