Green had been a disappointment in training camp, so the team terminated his contract. He signed with the Dolphins as an unrestricted free agent in March after spending four seasons with the Arizona Cardinals.
Smith, who has been practicing with the Dolphins' first-team defense, made an interception in Monday's preseason opener against the Jacksonville Jaguars. Davis, Miami's first-round draft choice in April, was flagged for three penalties in the game.
Green didn't remain unemployed for long. Citing league sources, NFL Network's Jason La Canfora reports that Green agreed to terms on a one-year deal with the San Francisco 49ers, who need cornerback depth after losing Walt Harris to a season-ending knee injury.
The Associated Press contributed to this report.