[4] As a senior at Oklahoma in 2014, Grissom was named an honorable mention for the All-Big 12 Conference after recording 39 tackles and 3.5 sacks on the year.

[7] On January 24, 2015, Grissom appeared in the Senior Bowl for Jacksonville Jaguars Gus Bradley's South team and assisted on three tackles during their 34–13 loss.

New England Patriots' head coach Bill Belichick stated that Grissom's tight end drills were, "As good as we saw all year.

"[10] At the conclusion of the pre-draft process, Grissom was projected to be a fifth or sixth round pick by NFL draft experts and scouts.

[16][17] Throughout training camp, he competed against Michael Buchanan, Jake Bequette, Zach Moore, and Xzavier Dickson.

[18] He was named the third right defensive end on the Patriots' depth chart to begin the regular season, behind Rob Ninkovich and Jabaal Sheard.

[19] He made his professional regular season debut in the Patriots' season-opener against the Pittsburgh Steelers and assisted on one tackle during their 28–21 victory.

He made his first career tackle with teammate Alan Branch on Steelers' running back DeAngelo Williams after he ran for a six-yard gain in the first quarter.

Grissom was inactive throughout the playoffs as the Patriots went on to lose in the AFC Championship to the eventual Super Bowl 50 Champions the Denver Broncos.

[21] He competed with Chris Long, Trey Flowers, and Frank Kearse throughout training camp for a backup defensive end role.