I'd check the rules if my internet didn't take about a half hour just getting to this page..
Anyways, Persuader isn't the sharpest tool in the shed, but his axe is basically > any axe in comics. There's maybe one or two example where it fails to cut something, but this is the one case where failing to defy logic is PIS.
Off the top of my head, it's cut off gravity with a swipe, darkness, a Sun Eater, dimensional barriers, various forms of energy... There's no real rhyme or reason on it's abilities, considering it's only an atomic axe.
But yeah, Persuader should own this. Terrax fires off a beam of Power Cosmic, and Persuader just ends up cutting the beam in half.. And maybe he cuts off the Power Cosmic in space with a simple swipe, so Terrax can't absorb anymore of it. Then he cuts through the axe, Terrax, the arena, and the fourth wall so Killermovies forum posters get to watch.