After the Hurricanes fell behind 21-0 in the first quarter, Sapp, an All-American defensive tackle at Miami in 1994, criticized Golden in a couple of tweets.
Sapp also questioned Golden's sideline attire, which generally consists of a shirt and tie.
Former Miami offensive lineman Leon Searcy, who was part of three national championship teams in 1987, '89 and '91, also criticized the Hurricanes' poor play against Clemson.
Joaquin Gonzalez, another former Hurricanes offensive lineman, also tweeted criticism toward Golden.
Miami athletics director Blake James has said he would wait until the end of the season to evaluate Golden's future.
Golden, who has a 32-24 record in his four-plus seasons at the school, has been under increasing criticism as attendance has dwindled at Miami's home games. After starting 3-0, the Hurricanes dropped consecutive road games against Cincinnati and Florida State earlier this month.
More than a few airplane banners calling for Golden's firing have been flown above Sun Life Stadium this season, including another on Saturday.