It turns out all you need is an ornery mule:
I see a couple of hounds in the upper left corner of the picture, and an empty rifle scabbard. From the sequence of pictures, it's not sure of the mule killed the cougar, or is just taking out his frustrations on it. Still, don't mess with an angry mule.
Heh, I had seen that picture and wondered the same thing. I hadn't noticed the empty scabbard though. In any case, that's one gutsy mule to grab hold of a cougar like that, even if it IS already dead. From what Hair has said of Bay's reaction to her big dog it sounds like he might be capable of the same thing.
I've seen that whole series of photographs too, and it's not clear, if I recall, whether the cougar is still alive in any of them, but you're right about the mule, I wouldn't mess with him. :~)