Joseph grew up in Pickering, Ontario, and attended Pickering High School in nearby Ajax, Ontario. He then attended Findlay Prep in Henderson, Nevada with his friend, AAU teammate, and future Texas Longhorn, Tristan Thompson. He increased his recruiting demand by leading Findlay Prep to the ESPN RISE NHSI Championship game in 2009 alongside Avery Bradley and Thompson, in which #2 ranked Findlay Prep defeated #1 ranked Oak Hill Academy 74–66. Joseph was named to the ESPN RISE NHSI All-Tournament Team. In Joseph's senior year, he and Thompson led the #2 ranked Findlay Prep Pilots to another ESPN RISE NHSI Championship in 2010 when they defeated #1 ranked Montverde Academy 59–46. He was named to the All-Tournament Team for the second consecutive year and was also awarded the tournament MVP. Joseph was ranked as the No. 7 prospect nationally by Rivals.com and No. 11 in the ESPNU 100 following his senior season. Joseph and Thompson then took part in the 2010 McDonald's All-American Game. Joseph also won the McDonald's Three Point Competition and was named a Jordan Brand Classic All-American. On April 23, 2010, Joseph committed to join Thompson at Texas. In August 2009, Joseph was selected to play in the 4th annual Boost Mobile Elite 24 basketball game at Rucker Park in New York City. This game showcases the top 24 high school basketball players in the nation regardless of recruiting class. On April 11, 2010, Joseph suited up for the World Select Team at the Nike Hoop Summit game against the United States Junior Select Team. The game was held at the Rose Garden in Portland, Oregon. Thompson and Enes Kanter, the third overall pick in the 2011 NBA draft, were also selected and joined Joseph on the World Select Team. The World Select Team lost 101–97. In Joseph's playing days at Pickering High School, he and his older brother Devoe Joseph teamed up and won back-to-back Ontario Provincial Championships by defeating their Greater Toronto Area rival, the Eastern Commerce Saints, in 2007 and 2008. In 2008, prior to leaving for Findlay Prep, Joseph was selected and participated in the annual All-Canada Classic All-Star Game, which gathers some of the top high school players in Canada.
Cory Joseph started all 36 games in his freshman season, leading the team in scoring four times and in rebounding twice. Joseph played one of his best games, recording his career high 21 points and a game-winning jumper December 18, 2010 against North Carolina. Texas entered 2011 NCAA March Madness as a four seed in the West Regional Division. Texas lost to fifth-seeded Arizona in the third round with a standout performance and game-winning shot from Derrick Williams. Following the end of the season, Joseph was considering entering the NBA draft, even with fellow countryman Myck Kabongo's decision to commit to Texas.
On June 23, 2011, Joseph was drafted 29th overall in the 2011 NBA Draft by the San Antonio Spurs. Fellow Canadian and Longhorn Tristan Thompson was drafted 4th overall by the Cleveland Cavaliers, becoming the highest Canadian born draftee in NBA history at that point. (Anthony Bennett was the 1st pick in the 2013 draft.) It was also the second time in NBA history that two Canadians were selected in the first round of the same draft, the first being in 1983 when Leo Rautins and Stewart Granger were selected 17th and 25th, respectively. The 2011 draft was also the first time three Texas Longhorn basketball players went in the first round after Joseph's former collegiate teammate Jordan Hamilton went 26th overall to Dallas Mavericks.
During the 2011–12 season, the Spurs assigned Joseph to the Austin Toros of the NBA D-League three times. He was also assigned to the Toros during the 2012–13 season. On February 4, 2013, Joseph was named to the Prospects All-Star roster for the 2013 NBA D-League All-Star Game. However, due to injury, he was replaced by Justin Dentmon.
In late February 2013, Tony Parker sustained an injury, and Joseph became the Spurs' starting point guard. In his first five starts, Joseph averaged 8.8 points and 2.6 assists while shooting 58.6 percent.
On June 15, 2014, Joseph won his first NBA championship after the Spurs defeated the Miami Heat 4 games to 1 in the 2014 NBA Finals.
Joseph's older brother, Devoe, played for the University of Minnesota before transferring to Oregon. Cory Joseph is also the second cousin of Kris Joseph, who was drafted by the Boston Celtics in 2012.