He played college football at Southern Methodist University and was signed by the Dallas Cowboys as an undrafted free agent in 2012.

Beasley attended Little Elm High School, where he was an option quarterback, leading the Lobos to the Texas UIL-4A playoffs in consecutive years.

[4] Beasley accepted a scholarship from Southern Methodist University, where he was converted into a wide receiver, playing in 11 games with seven starts as a freshman, while finishing third on the team with 42 receptions for 366 yards and three touchdowns.

[13][14] Beasley went undrafted in the 2012 NFL draft due to his size and was signed by his hometown team, the Dallas Cowboys.

[17] Beasley left abruptly during training camp, stating he was dealing with "personal stuff", and even considered retiring from professional football.

[25] In the Wild Card Round against the Detroit Lions, Beasley made four catches – three for first downs- for 63 yards and recovered a fumble in the 24–20 victory.

Beasley was eventually replaced by rookie Lucky Whitehead after having poor return averages and a critical muffed punt in a loss against the New York Giants.

[35] In the regular-season finale against the New York Giants, he caught six passes for 94 yards along with the game-winning touchdown in the narrow 36–35 road victory.

[44] Against the Dallas Cowboys, his former team, on Thanksgiving Day in Week 13, Beasley finished with six receptions for 110 yards and a touchdown as the Bills won on the road by a score of 26–15.

[53] During Week 12 against the Los Angeles Chargers, Beasley threw a touchdown pass to fellow wide receiver Gabe Davis on a trick play in the 27–17 victory.

[54] During Week 13 against the San Francisco 49ers on Monday Night Football, Beasley recorded nine catches for 130 yards and a touchdown during the 34–24 road victory.

[60] In the AFC Championship Game against the Kansas City Chiefs, Beasley recorded seven catches for 88 yards during the 38–24 road loss.

[64] During Week 6 against the Tennessee Titans, Beasley caught seven passes for 88 yards and his first touchdown of the season in the narrow 34–31 road loss.

[70] On September 24, 2022, Beasley was elevated to the active roster for a game against the Green Bay Packers before being demoted back to the practice squad two days later.

[86] In June 2021, Beasley announced on social media that while he understood the NFL's interest in players getting the COVID-19 vaccine, he would forgo it nonetheless, even if it meant that he would have to end his playing career as a result.

[88] Beasley later entered a public back and forth with teammate Jerry Hughes over the NFL's newly implemented vaccine rules.

[90] On August 25, Beasley and teammate Isaiah McKenzie were fined $15,000 for violating the NFL's COVID-19 protocol by not wearing masks.

[92] On October 4, 2021, Beasley took to his Twitter account to criticize Bills fans who booed him at games due to his unvaccinated status.

[94] On December 26, 2021, ESPN reported that Beasley had "been fined multiple times for COVID-19 protocol violations, reaching a cumulative sum in the range of $100,000.