Putz became a free agent one day after New York declined his $9.1 million option and chose to pay a $1 million buyout.
A total of 120 players have filed for free agency since the World Series, and about 60 more are potentially eligible to file by the Nov. 19 deadline.
Minnesota exercised a $10.5 million option for 2011 on outfielder Michael Cuddyer, who hit a career-high 32 homers last season and had 94 RBI. The option is part of a contract Cuddyer signed in 2008 that will pay him $33.5 million over four years. If the Twins had declined the option, they would have owed a $1 million buyout.