FL Statue 588.15 puts the owner responsible for their livestock in/about on a roadway or on the RoW.
FSS 588.24 Refusal or failing to remove your animals from RoW, is a 2d degree Misdemeanor offense.
FSS 588.16 Gives Authority to the Sherriff, etc... to impound livestock running at large. Says Nothing about authorizing the killing of the animal(s).
FSS 588.17 (4) (a) and (b) deals with disposing of the livestock and humanely if necessary. But that's After the animal has been impounded, and then too, only After Notifying the Owner of the impending disposal.
Also referring to the "laughter", you should remember, He was talking to a dispatcher, not an Officer.
That's why they transferred the call to a lieutenant. And since there were other inaudible voices heard on the tape, you really don't know if the dispatcher was laughing at that particular situation or laughing at a joke someone had just told?
It's hard to second guess the circumstances as to why this happened the way it did, but the fact he took no trailer or equipment to catch an animal (rope/lasso/herding dog) to start with, and the fact he told the dispatcher "It won’t be the first one I did", leaves one to believe he had no intention to remove the animal responsibly from the git-go.
Here's the Facts of the Case as we know it, You Decide.....
Philip Hayes charged for shooting donkey on Deaton Bridge Road (pnj.com)