Mm, if you can somehow give the stag negative levels without attacking it, each negative level makes it lose 5 hp without being "damage". So if you cast retributive enervation and the stag successfully melee attacks you with its bull rush, it loses 5hp. The only other way I can think of to impose negative levels without an attack is via holding aligned or bane weapons, and I don't recall any that would apply to the stag (if it could even hold one).