When a fly-ass dude spits beastly game at a female that be fine as a mutha-fucker, in other terms when an upstanding young gent (gentleman) attempts to court/woo a respectible, high-class young lady. Savaging also means doing things/acting in a Savage like way.
"dude you were savaging on that chick last night"
"i see pussy, savage pound it"
"He's savaging right now"