Buttó signed with the New York Mets as an international free agent on June 2, 2017. He made his professional debut with the Dominican Summer League Mets, posting a 1.44 ERA across 15 appearances (8 starts).[1] In 2018, he split time between the rookie–level Kingsport Mets and Low–A Brooklyn Cyclones, making 12 appearances (11 starts) and recording a 3.86 ERA with 55 strikeouts in 60+2⁄3 innings of work.[2]
Buttó spent the entirety of the 2019 season with the Single–A Columbia Fireflies. In 27 games (25 starts), he went 4–10 with a 3.62 ERA and 109 strikeouts in 112.0 innings pitched.[3] Buttó did not play in 2020, as the minor league season was cancelled after the COVID-19 pandemic struck.[4] He returned to action in 2021, making 20 combined starts between High–A Brooklyn and the Double–A Binghamton Mets. In 98+2⁄3 innings of work, Buttó posted a 4–6 record and 3.83 ERA with 110 strikeouts.[5]
On November 19, 2021, the Mets added Buttó to their 40-man roster to protect him from the Rule 5 draft.[6] Buttó was assigned to the Double–A Binghamton Mets to begin the 2022 season, and posted a 6–5 record and 4.00 ERA with 108 strikeouts across 20 games (18 starts).[7]
On August 21, 2022, Buttó was promoted to the major leagues for the first time, to make a spot start against the Philadelphia Phillies.[8] In his debut, Buttó allowed 7 runs on 9 hits and 2 walks across 4.0 innings of work.[9] He was optioned back to Triple–A Syracuse the following day.[10] In 8 games (7 starts) for Syracuse, Buttó registered a 2.45 ERA with 30 strikeouts in 36+2⁄3 innings pitched.[11]
Buttó was optioned to the Triple-A Syracuse Mets to begin the 2023 season.[12] He returned to the major leagues several times across the season, with his longest stay coming after the September roster expansion. Over 9 games (7 starts) for the major league team in 2023, Buttó recorded a 1–4 record and a 3.64 ERA, with 38 strikeouts across 42 innings pitched.[13]
Buttó was again optioned to Triple–A Syracuse to begin the 2024 season after he was beaten out by Tylor Megill for the final rotation spot.[14] After injuries to multiple members of the Mets' starting staff, Buttó was quickly brought back to the major leagues on April 4 as the 27th man on the roster to start one game of that day's doubleheader. After the game, Carlos Mendoza told the media that Buttó had earned more opportunities.[15] In seven starts before being sent down to Syracuse on May 14, he posted a 3.08 ERA with 38 strikeouts in 38 innings.[16]
On July 2, 2024, Buttó was called up from Syracuse to replace reliever Tyler Jay in the depleted bullpen. That day he pitched two scoreless innings and got the win in a 7-2 game against the Washington Nationals.[16] He recorded his first major league save on July 10 in a 6-2 win over the Nationals.[17] In 2024, across 37 games as a starter and a reliever, Buttó posted a 7-3 record, a 2.55 ERA, and 79 strikeouts across 74 innings pitched.[18]