Rodriguez went 62-for-69 on save chances for the Los Angeles Angels, breaking the record of 57 saves set by Bobby Thigpen in 1990. K-Rod was 2-3 with a 2.24 ERA for the only team in the majors to win 100 games.
Vizquel filed after San Francisco declined a $5.2 million option, choosing to pay a $300,000 buyout.
Floyd hit .268 with 11 homers and 39 RBIs in 72 starts this season. The Rays held a $3 million option with a $250,000 buyout on the 35-year-old slugger, who was on the postseason roster until a right shoulder injury sidelined him for the final two games of the World Series loss to Philadelphia.
The club held a $2 million option with a $400,000 buyout on Miller, who was 2-0 with a 4.15 ERA and two saves in 68 games. The 35-year-old lefty has made at least 60 appearances in each of the past six seasons.
Floyd and Miller are in the group of players still eligible to file for free agency by the Nov. 13 deadline. Free agents can start negotiating money with all clubs the following day.
Mike Cameron's $10 million option was exercised by the Milwaukee Brewers, preventing him from becoming eligible to file. The Brewers could have paid a $750,000 buyout to the three-time Gold Glove winner, who batted .243 with 25 home runs and 70 RBIs this season.
Also, San Diego general manager Kevin Towers said at the GM meetings in California that the Padres probably will exercise outfielder Brian Giles' $9 million option by Saturday's deadline and are trying to work out an agreement to keep closer Trevor Hoffman.