Murphy was selected in the sixth round of the 2019 MLB draft by the Boston Red Sox.[6] After signing with the team, he was assigned to the Low-ALowell Spinners and posted a 1.08 ERA with 34 strikeouts in 33+1⁄3 innings pitched.[7] He did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[8] Murphy began the 2021 season with the High-AGreenville Drive before being promoted to the Double-APortland Sea Dogs.[9] Overall with both teams during 2021, Murphy made 21 appearances (20 starts), compiling a 4.62 ERA and 8–5 record while striking out 128 batters in 101+1⁄3 innings.[10]
Murphy began the 2022 season with Portland.[11] He made his Triple-A debut with the Worcester Red Sox on June 30.[12] Overall with both teams, Murphy pitched to a 7–11 record in 30 games (28 starts), posting a 4.03 ERA while striking out 149 batters in 152 innings.[10]
On November 15, 2022, the Red Sox added Murphy to the 40-man roster to protect him from the Rule 5 draft.[13] Murphy was optioned to Triple-A Worcester to begin the 2023 season.[14] In 10 games (9 starts) for Worcester through early June, Murphy registered a 7.71 ERA with 42 strikeouts in 39+2⁄3 innings pitched.[15] He was added to Boston's active major-league roster on June 6.[16] He made his MLB debut the following day, pitching 3+1⁄3 innings of scoreless relief again the Cleveland Guardians.[17] He was optioned back to Worcester on June 8,[18] was briefly on Boston's roster for a doubleheader on June 18,[19] and was recalled on June 23.[20] Murphy impressed in his first long stint with Boston, serving primarily as a bulk reliever.[21] On August 11, Murphy earned his first major-league save, pitching three shutout innings aganist the Detroit Tigers.[22] He split time between Boston and Worcester during the second-half of August and during September.[23][24]
Murphy was placed on the 60–day injured list to begin the 2024 season after suffering a left UCL sprain in his left elbow.[25] He underwent Tommy John surgery on April 10, 2024, ending his season.[26]