However, only to the animal itself; not the hearthling.
I just ended up killing a mouflon because it refused to yield, hitting it with a left hook and dealing 32 damage which killed it. Not sure what I could have done here to prevent it given that I didn't have punch in my deck.
Seems weird that you're forced to use a weaker character just to not murder an animal while you kill it, so either mouflons should have a higher fear level (1/3 hp = yield) or the damage dealt while taming shouldn't count as real damage (If you're taming, you're not going to kill the animal you're beating sense into)
And no, I didn't beat it beyond yield, I set my yield to on before the fight started and used lower damage attacks until the end, the instant it died it showed: 32 in red (Damage) 45 in yellow (Tame %) and then 0 in yellow (Tame set to 0 because it died)