Joseph graduated from Hays High School, where he played baseball, football and basketball for the Rebels in 2006. He pitched for the Houston Cougars, from 2007 to 2009. In 2007 as a freshman, he went 1-1 with a 6.42 ERA, striking out 23 in 54.2 innings in 18 games. In 2008 as a sophomore, he went 2-1 with a 5.72 ERA, striking out 40 in 56.2 innings. In 2009 as a junior, he was used as a reliever, where in 31 appearances, he went 3-1 with a 2.16 ERA and 11 saves, striking out 75 in 50 innings. He was drafted in the 3rd round by the Cincinnati Reds in the 2009 MLB Draft.
Professional career
Cincinnati Reds
He was assigned to Advanced Rookie Billings, where he pitched in 8 games before earning a promotion to Single-A Dayton on July 22, where he pitched in 16 games before the end of the season. In 24 games in 2009, he went 4-3 with a 3.06 ERA, striking out 42 in 32.1 innings. Joseph began 2010 with the Dragons before earning a promotion to High-A Lynchburg on May 27, where he pitched in 31 games. At the end of the season, he earned a promotion to Double-A Carolina, where he pitched in 7 games. In 57 games in 2010, he went 3-5 with a 2.08 ERA and 24 saves, striking out 103 in 65 games. After the year, he was named Cincinnati's Minor League Pitcher of the Year. Joseph went to spring training with the Reds in 2011, where he pitched in 5 games, giving up 8 runs in 5.1 innings. Joseph pitched all of 2011 with Carolina, where in a league-leading 57 appearances, he went 1-3 with a 6.94 ERA, striking out 66 in 58.1 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 innings. Joseph began 2012 with Double-A Pensacola, where he pitched in 26 games before earning a promotion to Triple-A Louisville on June 9. He was a Southern League Mid-Season All-Star. He pitched in 18 games with the Bats before being traded.
On July 31, 2012, he was traded to the Kansas City Royals with J. C. Sulbaran for Jonathan Broxton. He was assigned to Triple-A Omaha, where he finished the season. In 55 games in 2012, he went 9-3 with a 2.33 ERA, striking out 87 in 69.2 innings. He was added to the Royals' 40-man roster on November 20, 2012. Joseph began 2013 with Omaha before his promotion. On July 11, Joseph was promoted to Kansas City, replacing Wade Davis, who was on paternity leave. He made 2 appearances before being optioned to Omaha 2 days later in favor of a fresher arm, lefty Everett Teaford. His first Major League strikeout was of Jason Kipnis. On August 10, he was recalled, and he made an appearance that day against Boston, but he was optioned the next day. After Omaha's season ended, Joseph was recalled on September 3 after the rosters had expanded. In 47 games with Omaha, he went 4-3 with a 3.95 ERA, striking out 84 in 54.2 innings. He pitched in 3 games with the Royals in September to end the season. In 6 games with Kansas City in 2013, he finished 2 games, giving up 4 hits and 0 runs with 7 strikeouts in 5.2 innings.
Joseph was designated for assignment by the Royals on June 24, 2014. He was acquired by the Miami Marlins for cash considerations six days later. On March 24, 2015, Joseph was released by the Marlins.
