Mullins was born in New Orleans, Louisiana. He and his family lost their home after Hurricane Katrina hit New Orleans in 2005, forcing them to take refuge in Brookhaven, Mississippi and Baton Rouge, Louisiana. He played club soccer for Chicago Fire Juniors from 2007 to 2009, winning the state title in each of the three years and was rated the no. 31 recruit in the nation by Top Drawer Soccer. Mullins graduated from Jesuit High School in New Orleans.
On March 2, 2010, it was announced that Mullins had signed a letter of intent to play college soccer at the University of Maryland along with four others. In his freshman year with the Terrapins, Mullins made 21 appearances for the club. On September 14, he scored his first collegiate goal in a 3–0 victory over Loyola University Maryland. A month later, he netted the game-winner in the Terps 1–0 upset victory over no. 2-ranked UConn. He also scored in his NCAA tournament debut on November 21 against the University of Pennsylvania. Mullins finished the year with five goals and four assists and was named ACC Freshman of the Year. He was also named to Top Drawer Soccer's All-Rookie Second Team.
In 2011, Mullins made a switch from midfielder to striker and excelled. He made 21 appearances and tallied six goals and three assists, including one on November 27 against Louisville in the third round of the NCAA Tour. Maryland lost the match, 4–2. He was named Second-Team All-ACC. In 2012, Mullins became one of the leaders for the Terps as he appeared in all 24 games for the club, starting in 23 of them. On October 19, he assisted on an overtime game-winner by Schillo Tshuma that gave the no. 1-ranked Terps a 1–0 victory over no. 2-ranked North Carolina. A week later, he scored in Maryland's 2–2 draw with Clemson which was good enough to win the ACC regular-season title. On November 8, Mullins earned a pair of ACC honors as he was named ACC Offensive Player of the Year and First Team All-ACC. Three days later, Mullins was named ACC tournament MVP after the Terps defeated North Carolina 2–1 to win the ACC tournament title. Mullins finished the year with 17 goals and 10 assists.
On January 11, 2013, Mullins was awarded the Hermann Trophy. Despite rumors that he would sign a Generation Adidas contract and enter the 2013 MLS SuperDraft, Mullins decided to stay at Maryland for his senior season. In his final season with the Terps, Mullins led the team to back-to-back ACC regular season and Tournament titles as well as a trip to the College Cup. On December 13, he scored both of Maryland's goals in a 2–1 victory over 8th-seeded Virginia in the semifinal. Two days later, he scored the opening goal in the national title game against 3rd-seeded Notre Dame. However, the Fighting Irish would come back with two unanswered goals to defeat Maryland, 2–1. On January 10, 2014, Mullins won his second straight M.A.C. Hermann Trophy, making him the fourth male in NCAA history to win the award in back-to-back seasons.
Mullins also spent time in the USL Premier Development League with the Baton Rouge Capitals in 2007, and with New Orleans Jesters in 2011 and 2012.
Mullins was selected 11th overall by the New England Revolution in the 2014 MLS SuperDraft. On May 3, in his second professional game, Mullins scored his first professional goal.
On December 10, 2014, Mullins was selected by expansion club New York City Football Club. Mullins was the fourth overall pick of the expansion draft where NYCFC and Orlando City SC selected players from other teams' list of "Unprotected Players". Mullins will be joined at NYCFC by another Revolution player, Tony Taylor. On March 15, 2015, Mullins played his first game for New York City FC, coming on as an 84th-minute substitute against his former team, the New England Revolution, and scored on his first touch to make the score 2–0, after a pass from David Villa.
Mullins was traded to D.C. United on July 20, 2016 for General Allocation Money, Targeted Allocation Money, and an International Roster Spot for the 2016 and 2017 season.As of match played 18 October 2016
Atlantic Coast Conference Freshman of the Year: 2010
First team All-ACC: 2012
ACC Offensive Player of the Year: 2012