Morrissey grew up in Huntingdon Valley, Pennsylvania and attended La Salle College High School.
[1] Morrissey was lightly recruited coming out of high school and received no NCAA Division I Football Bowl Subdivision offers.
[1] Morrissey started the first 11 games of his redshirt sophomore season before suffering a season-ending injury and was named third-team All-Atlantic Coast Conference (ACC).
[5] As a redshirt senior, Morrissey started all 11 of Pittsburgh's games, including one at right guard after an injuries to that position, and was named second-team All-ACC and was awarded the Burlsworth Trophy as the best player in Division I football who began his college career as a walk-on.
[15] He made his NFL debut on November 7, 2021, as the team's starting center in a 9–17 loss to the Miami Dolphins.