Gragg played as a wide receiver for Warren High School, and converted to a tight end after his freshman season at the University of Arkansas.

[4] Gragg played football as a wide receiver for Warren alongside future NFL players Jarius Wright and Greg Childs.

[7][12] During the second game of the season, against the Louisiana–Monroe Warhawks, Gragg caught a 25-yard pass from quarterback Casey Dick on fourth down and one to continue a drive that ended with a game-winning touchdown.

[21] In the Razorbacks' eleventh game of the season, Gragg caught 8 passes for 119 yards, both single-game career highs, as the team defeated the Mississippi State Bulldogs and moved to a 10–1 record.

[30] In July 2012, Gragg was listed as a preseason nominee for the John Mackey Award, a recognition presented annually by the Nassau County Sports Commission to the best tight end in college football, and was voted to the second team of the Coaches Preseason All-Southeastern Conference (SEC) squad, an honorific roster composed of the second-best players in the SEC.

[31][32] In July, ESPN writers Edward Aschoff and Chris Low ranked Gragg as the best tight end in the conference.

[33] In Arkansas' season opener against the Jacksonville State Gamecocks, Gragg accumulated 110 yards and two touchdowns over 7 catches, a performance for which he earned the John Mackey Tight End of the Week award.

[45][46] In September 2013, ESPN columnist Mike Rodak gave the Bills a C grade in tight end depth on an A–F scale and said Gragg "would be in the bottom 10 percent of NFL starters at [the position]".

[46] Gragg made his regular-season NFL debut on October 13 against the Cincinnati Bengals, and caught his first career reception and touchdown against the Pittsburgh Steelers four games later.

[48] Prior to the Bills' 2014 training camp, Rodak gave Gragg a 45% chance to make Buffalo's 53-man roster: Rodak described him as "the most athletic tight end" with the Bills, but also wrote that "there might not be a spot for Gragg" with tight ends Tony Moeaki, Scott Chandler, and Lee Smith on the team.

[50] In the fourth quarter of the Bills' regular-season October 5 matchup against the Detroit Lions, Gragg caught a touchdown pass that, with an added two-point conversion, tied the game; Buffalo won the contest, 17–14, and moved to a 3–2 record.

[51][52] When he attempted to catch a low-thrown pass in the second half of a game against the New York Jets on November 24, Gragg injured his right knee, which caused him to miss the remainder of the Bills' season.

[53] During 2014, over the ten games in which he played, Gragg accumulated 7 receptions for 48 yards and a touchdown as Buffalo finished with a 9–7 record, second in the AFC East behind the New England Patriots.

[63] In a preseason game against the Philadelphia Eagles, Gragg suffered an ankle injury after a 20-yard catch; he was placed on the Jets' injured reserve list on September 1, 2017.