Beck, 27, pitched three innings for the Mets out of the bullpen on Sunday in the team’s 9-0 loss to the Tampa Bay Rays. He yielded two runs in the process.
For Beck, he will end his Mets career with a 5.23 ERA in six games.
The Georgia native spent the past three plus seasons with the Chicago White Sox. Last year, he pitched to a 6.40 ERA in 57 appearances.
As for Blevins, the 34-year-old has pitched in 35 games for New York this year and has registered a 4.79 ERA.
He is a free agent at year’s end.