He spent 2019 with the rookie-level Pulaski Yankees, making 11 starts and recording a 3.29 ERA with 53 strikeouts in 54.2 innings pitched.
[3] In 2021, he pitched for the Single-A Tampa Tarpons, High-A Hudson Valley Renegades and Double-A Somerset Patriots.
In 23 appearances (21 starts) between the three affiliates, Vásquez pitched to an 8–4 record and 2.52 ERA with 130 strikeouts in 107.1 innings of work.
On May 25, 2023, the Yankees announced that Vásquez would be promoted to the major leagues for the first time to start the following day against the San Diego Padres.
[9] On December 6, 2023, the Yankees traded Vásquez, Michael King, Drew Thorpe, Jhony Brito, and Kyle Higashioka to the San Diego Padres for Juan Soto and Trent Grisham.