TMZ Sports has obtained new video of Terrelle Pryor's post-game blowup from Monday night ... revealing the Redskins star got heated over insults about his alma mater.

In the new video, you can hear the fan say, "Hey Terrelle, you bitch! F*ck you! F*ck Ohio State!!"

Of course, Pryor played for the Buckeyes from 2008 to 2010 -- right before he was hit with a 5-year ban from OSU football amid an NCAA investigation into players receiving improper benefits.

Clearly, he's still proud of his school -- and launched his middle finger and an F-bomb after the Ohio State insults.

Pryor was also upset because his Skins lost to the Chiefs in Kansas City.