Claggett attended Palm Springs High School, where he was primarily a shortstop in baseball and a forward in basketball.

[3] Claggett was originally selected by the Detroit Tigers in the 11th round of the 2005 Major League Baseball Draft.

[4][5] That year, he pitched to a 4.03 ERA with 25 strikeouts and seven saves in 22.1 innings for the Oneonta Tigers in the Short Season Single-A New York-Penn League.

Claggett started the 2006 season with the West Michigan Whitecaps in the Midwest League, maintaining a 0.91 ERA with 58 strikeouts and 14 saves in 59.1 innings.

[7] The New York Yankees acquired him from Detroit, along with right-handed pitchers Humberto Sánchez and Kevin Whelan, in exchange for outfielder Gary Sheffield on November 10, 2006.

[9] He began the 2008 season on the disabled list with a left hamstring strain, then made one appearance with Tampa before being promoted to Double-A Trenton.

[13] Claggett made his major league debut that day, allowing eight runs on nine hits in 12⁄3 innings to the Cleveland Indians.

Claggett was called up again on August 5[16][17] and allowed two runs on two hits and two walks in an inning of work against the Boston Red Sox the following day.

[43] Returning to the collegiate level, Claggett was pitching coach and recruiting coordinator at Riverside City College in 2016.

[44] Claggett moved up to the NCAA Division I level in 2017 as volunteer assistant coach at San Jose State under manager Jason Hawkins.

[47] They stayed with the Cougars for four years before joining Wichita State University in 2023, where he will serve as pitching coach and recruiting assistant.