Vesia, 27, struggled to start the season, going 0-2 with a 7.84 ERA over his first 13 relief outings before he was optioned May 3 when Stone was called up to join the rotation. In 10 outings at Oklahoma City, Vesia was 1-1 with a 4.66 ERA.
A mainstay of the Dodgers' bullpen the previous two seasons, Vesia is 8-4 with a 3.39 ERA in 122 career relief outings over the past four seasons for the Miami Marlins (2020) and Dodgers (2021-23).
Stone, 24, struggled in his first stint in the major leagues, with a 14.40 ERA over three starts.
The move to send Stone down is likely an indication that right-hander Michael Grove (groin) is closing in on a return from the injured list.