Joseph was born and raised in Montreal, Quebec, where he grew up in the working-class neighbourhood of Cote-des-Neiges north of downtown.

[2] Joseph played in Maurice's shadow for a number of years as the older star gained prominence at noted Montreal-area prep school Champlain St. Lambert College.

He worked on his game, grew to 6-foot-6 and became a star for Sun Youth, a club-team powerhouse in the Montreal Basketball League.

[4] On a recommendation from youth coach Henry Wong, who thought Joseph needed an athletic and academic challenge, Joseph's mother agreed to let him leave Montreal in 2006 to complete two years of high school at Archbishop Carroll in Washington, D.C.[5] As a senior, Joseph led Archbishop Carroll to a 26–11 record, including a 21-point, five rebound, three assist and three block effort in the Washington Catholic Athletic Conference (WCAC) Tournament in a 65–55 win over Our Lady of Good Counsel.

[10] After an injury to Paul Harris, Joseph would receive the first start of his career against South Florida on January 2, 2009, scoring seven points and adding three rebounds.

In SU's Big East opener against Seton Hall on December 29, 2009, Joseph scored 16 points, including 8-of-9 shooting from the free throw line in an 80–73 win.

[13] Joseph finished with averages of 11.0 points and 5.4 rebounds on the season, and was named the Big East Conference Sixth Man of the Year.

He was named in the Wooden Award Preseason Top 50 list and improved his numbers across the board, leading Syracuse in scoring at 14.3 points per game and placing second in rebounding (5.2) and steals (1.5).

Joseph was named Most Outstanding Player of the tournament with averages of 19.0 points, 9.5 rebounds and 3.5 steals in wins against Virginia Tech and Stanford.

[19] He led the Orange in scoring during the regular season (13.4 ppg) and received an array of post-season awards, including a spot on the 2012 All-Big East First Team.

Additionally, Joseph was one of 15 post-season finalists for the Wooden Award, making him among the most decorated Canadians ever to play NCAA Division I basketball.

[23] On July 5, 2012, the Boston Celtics announced that Joseph was added to their roster for the 2012 Orlando and Las Vegas NBA Summer League's.

[31] Joseph was traded back to his draft team the Boston Celtics on July 12, 2013, along with Keith Bogans, Kris Humphries, MarShon Brooks and Gerald Wallace as well as three first-round picks in a blockbuster deal that sent Celtics stars Kevin Garnett, Paul Pierce and Jason Terry to the Nets.