Cincinnati Reds

Joseph was drafted in the 3rd round (88th overall) by the Cincinnati Reds in the 2009 Major League Baseball draft. Joseph was assigned to the Advanced-Rookie Billings Mustangs, where he pitched in 8 games before earning a promotion to the Single-A Dayton Dragons 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 the High-A Lynchburg Hillcats on May 27, where he pitched in 31 games. At the end of the season, he earned a promotion to the Double-A Carolina Mudcats, 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.^[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 innings. Joseph pitched all of the 2011 season 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 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. He was a Southern League Mid-Season All-Star. He pitched in 18 games with the Bats before being traded.

Kansas City Royals

On July 31, 2012, he was traded to the Kansas City Royals alongside J. C. Sulbaran in exchange for Jonathan Broxton.^[2] He was assigned to the Triple-A Omaha Storm Chasers, 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.^[3] Joseph began 2013 with Omaha before his promotion.

On July 11, 2013, Joseph was promoted to the major leagues for the first time, replacing Wade Davis, who was on paternity leave.^[4] He made his MLB debut that day, pitching a scoreless third of an inning against the New York Yankees. He made another appearances before being optioned to Omaha 2 days later in favor of a fresher arm, southpaw Everett Teaford. His first Major League strikeout was of Cleveland Indians infielder Jason Kipnis. On August 10, he was recalled, and he made an appearance that day against the Boston Red Sox, 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, having only made one appearance for the big league team that year in which he allowed 6 earned runs in 2 thirds of an inning.^[5]

Miami Marlins

On June 30, 2014, Joseph was traded to the Miami Marlins in exchange for cash considerations.^[6] On July 31, Joseph was designated for assignment by Miami^[7] and later outrighted to the Triple-A New Orleans Zephyrs. He finished the year with New Orleans, but struggled to a 9.58 ERA in 9 appearances. On March 24, 2015, Joseph was released by the Marlins organization.^[8]

New Jersey Jackals

On April 17, 2015, Joseph signed with the New Jersey Jackals of the Can-Am League.^[9] In 35 appearances with the Jackals, Joseph logged a 3–3 record and 5.49 ERA with 51 strikeouts in 41.0 innings pitched. On January 20, 2016, Joseph was released by New Jersey.^[10]

Rockland Boulders

Joseph signed with the Rockland Boulders of the Can-Am League prior to the 2016 season. On June 28, Joseph was released by the team.^[11] On July 30, Joseph re-signed with Rockland.^[12] In 18 total games for the Boulders, Joseph logged a 7.16 ERA. He became a free agent after the 2016 season.