Blue, a 6'4" shooting guard from Madison, Wisconsin, originally committed to the University of Wisconsin, but received press coverage as he decommitted after becoming disenchanted by negative posts on Wisconsin Badgers internet message boards. Blue ended up enrolling at Marquette for the 2010–11 season. Blue was a key rotation player as a freshman and sophomore, and stepped into a starting role in his junior season. He averaged 14.8 points per game and was named second team All-Big East Conference.
After the season, Blue bypassed his senior season and declared his eligibility for the 2013 NBA draft.
After going undrafted in the 2013 NBA draft, Blue joined the Houston Rockets for the Orlando Summer League and the Memphis Grizzlies for the Las Vegas Summer League. On September 27, 2013, he signed with the Philadelphia 76ers. However, he was later waived by the 76ers on October 25 after appearing in five preseason games. Five days later, Blue signed with Maccabi Rishon LeZion of the Israeli Super League. On December 31, 2013, he was released by Maccabi after appearing in just seven games.
On January 14, 2014, Blue was acquired by the Delaware 87ers of the NBA Development League.
On January 22, 2014, Blue signed a 10-day contract with the Boston Celtics. He made his NBA debut later that day, recording 2 points, 2 rebounds and 1 assist in a 113–111 win over the Washington Wizards. On January 31, he was assigned to the Maine Red Claws. The Celtics did not offer Blue a second 10-day contract after his first 10-day contract expired, thus parting ways with both the Celtics and Red Claws. On February 1, he was reacquired by the 87ers. On March 7, he was traded to the Idaho Stampede in a four-team deal, and played out the rest of the 2013–14 season with the team. Blue appeared in 27 D-League games for three teams in 2013–14, averaging 16.8 points, 4.4 rebounds, 2.9 assists and 1.3 steals per game.
In July 2014, Blue joined the San Antonio Spurs for the 2014 NBA Summer League. On September 29, 2014, he signed with the Washington Wizards. However, he was later waived by the Wizards on October 3. On October 30, he was reacquired by the Idaho Stampede. The next day, he was traded to the Los Angeles D-Fenders in exchange for a second round pick (36th overall) in the 2014 NBA Development League Draft. On February 12, 2015, he was named to the Futures All-Star team for the 2015 NBA D-League All-Star Game as a replacement for Jordan Hamilton.
On April 13, 2015, Blue signed with the Los Angeles Lakers to help the team deal with numerous injuries. The Lakers had to use an NBA hardship exemption in order to sign him as he made their roster stand at 16, one over the allowed limited of 15. Due to the severe lack of guard depth, in the two games he played for the Lakers, he logged 26 and 48 minutes respectively.
In July 2015, Blue joined the Chicago Bulls for the 2015 NBA Summer League. On October 31, he was reacquired by the Los Angeles D-Fenders. On January 29, he was named in the West All-Star team for the 2016 NBA D-League All-Star Game, earning his second straight All-Star nod. At the season's end, he was named to the All-NBA D-League First Team.
In July 2016, Blue joined the Dallas Mavericks for the 2016 NBA Summer League. The following month, he had a one-game stint in China with the Guangxi Weizhuang Rhinos before returning to the US and re-joining the Los Angeles D-Fenders on October 30, 2016. On February 6, 2017, he was named in the Western Conference All-Star team for the 2017 NBA D-League All-Star Game, earning his third straight All-Star nod. On April 24, 2017, he was named the recipient of the NBA Development League Most Valuable Player Award for the 2016–17 season. He ranked third in the league in scoring with 24.8 points per game and added 5.1 rebounds, 3.0 assists and a team-high 1.6 steals in 47 games (46 starts). He was twice named Player of the Week during the season and helped the D-Fenders finish tied for the best record in the Western Conference at 34–16. Blue scored at least 30 points 10 times and reached the 40-point mark twice. On March 29, he made an NBA D-League-record 23 free throws en route to a season-high 41 points to go with seven rebounds and five steals in a 139–132 road victory over the Reno Bighorns.
On August 4, 2017, Blue signed with the Los Angeles Lakers, returning to the franchise for a second stint.