Miami released Core (undisclosed) with a non-football injury Tuesday, according to the team's official Twitter account.
The Dolphins signed Core to a reserve/future contract Tuesday.
The Dolphins signed Core to their practice squad, Aaron Wilson of Sportstalk 790 Houston reports.
Core (Achilles) tried out with the 49ers on Tuesday, Aaron Wilson of Sportstalk 790 Houston reports.
The Giants cut Core (Achilles) on Monday, Ralph Vacchiano of SportsNet New York reports.
The Giants shifted Core (Achilles) to injured reserve Wednesday
Core is believed to have suffered an Achilles tear during Tuesday's practice, Jordan Raanan of ESPN.com reports.
The Giants and Core agreed to terms on a contract Tuesday, Tom Pelissero of NFL Network reports.
Core didn't receive a target in Monday's 37-18 loss to the Cowboys.
Core caught three of five targets for 28 yards in Sunday's 28-14 loss to the Bills.