Mate and I on a night ride one night waiting to cross a country road as a car approached. Just as the car got there a rabbit hopped out and the car went straight over it, leaving it in the middle of the road trying to drag its mangled back legs behind it.
I looked at my mate and said ‘we can’t leave it like that’ to which he replied ‘I agree. I’ll hold your bike’
So I picked it up, every intent to stretch its neck as above, until it occurred to me I had no idea how, or how hard to pull. The vision of a Lycra clad bloke standing in the middle of the road daubed in blood and holding both halves of a decapitated rabbit flashed before me. ‘Ere Sarge; did you see what I think I saw?’
So I held it tight around the waist (legs were ****) and smashed its head hard 2 or 3 times on a fence post, it stopped wriggling, and foxy got a free meal.
Grim as it was I couldn’t have walked away like the op though. Whack it hard on the back of the neck / base of the skull with the heel of your shoe, or a seat post if you can’t wring its neck. And I mean hard, its supposed to be fatal, not tickle.