[1][2] The New York Yankees selected Toffey in the 23rd round of the 2014 MLB draft, but he enrolled at Vanderbilt rather than sign.

[5][6][7] The Baltimore Orioles selected Toffey in the 25th round of the 2016 MLB draft, but he again did not sign, returning to Vanderbilt for his junior year.

[9] On July 21, 2018, the Athletics traded Toffey, along with Bobby Wahl, to the New York Mets in exchange for Jeurys Familia.

On July 2, 2021, the Mets traded Toffey to the San Francisco Giants in exchange for Anthony Banda.

[18] He was sent back down after the game without making his debut and sent outright off of the 40-man roster to Lehigh Valley after he cleared waivers on July 16.

[20] Toffey's father, Jack, played college and professional baseball and works as a sports agent.