The 24-year-old Yamamoto was 4-5 with a 4.46 ERA in 15 starts in 2019, striking out 82 and walking 36 in 78 2/3 innings. He was 0-1 with an 18.26 ERA in 11 1/3 innings over three starts and one relief appearance during the pandemic-shortened 2020 season.
Yamamoto had a $565,000 salary in the majors last year and $173,368 in the minors, and he earned $98,849 in prorated pay.
The 19-year-old Polanco has hit .244 in 450 at-bats in two minor league seasons with 20 doubles and 50 RBIs. He split 2019 between the Dominican Summer League and the Gulf Coast League.
New York opened a roster spot for Yamamoto by designating infielder Robel García for assignment. The 27-year-old was claimed off waivers from Cincinnati last Oct. 26. He hit .208 with five homers and 11 RBIs in 72 at-bats over 31 games for the Chicago Cubs in 2019.