The 30-year-old Ramos pitched 43 games for the Rays last season, including seven starts. He was 2-6 with a 3.70 ERA. He was tied for seventh among AL relievers with 13 outings of at least two innings.
Ramos is 5-11 with one save and a 3.90 ERA in 186 games for San Diego and Tampa Bay.
The 23-year-old Sappington went a combined 4-11 with a 6.02 ERA in Double-A and Single-A last season.