Joseph graduated from Hays High School, where he played baseball, football and basketball for the Rebels in 2006.

Joseph began 2010 with the Dragons before earning a promotion to the High-A Lynchburg Hillcats on May 27, where he pitched in 31 games.

[1] Joseph went to spring training with the Reds in 2011, where he pitched in 5 games, giving up 8 runs (5 earned) in 5+1⁄3 innings.

After the year, Joseph pitched in the Arizona Fall League with Phoenix, where, in 12 appearances, he went 1–1 with a 2.16 ERA, striking out 17 in 16+2⁄3 innings.

Joseph began 2012 with the Double-A Pensacola Blue Wahoos, where he pitched in 26 games before earning a promotion to the Triple-A Louisville Bats on June 9.

On July 31, 2012, he was traded to the Kansas City Royals alongside J. C. Sulbaran in exchange for Jonathan Broxton.

On July 11, 2013, Joseph was promoted to the major leagues for the first time, replacing Wade Davis, who was on paternity leave.

He made another appearances before being optioned to Omaha 2 days later in favor of a fresher arm, southpaw Everett Teaford.

Joseph was designated for assignment by the Royals on June 24, 2014, having only made one appearance for the big league team that year in which he allowed 6 earned runs in 2⁄3 of an inning.