The name for the Texas Longhorn mascot at the University of Texas at Austin. The name was derived after a loss to UT's oldest 'rival', the Aggies. The rare loss to A&M led to a prank in which the school mascot was branded with 13-0, the final score of the game. The Longhorns turned it around and named the mascot Bevo.
To get screwed, or "bent over" by an over-zealous, over-reaching person or entity. Someone who would stab their own mother in the back for the change in her pocketbook. Treasonous and domineering.
A gay connotation may or may not apply, depending on the situation.
Did you hear? Our company is in the middle of a hostile takeover bid...we're gonna get Bevo'd.
His gay lover pimp-slapped and then went all Bevo on him.