Good. She should. I have not read her book but from the quotes from it I have seen so far (from those who have read it) she seems to take pride in this decision. It is not a bad day or a challenge or painful decision nor does she remark on any lessons she learned from it.
I might be wrong though.
According to Noem in the Tweet I referenced above, it is and was legal in SD to put down a dog who attacks and kills livestock.
While it’s clearly true that farmers find it necessary to kill animals they own on their property as part of their job, and that is legal, Noem pointing that is completely missing the point. What would be the illegal in the UK was the unnecessary suffering. Blasting away with your shotgun at some poor unfortunate animal is not humane euthanasia. What is described with the goat, where Noem left it in agony while she went to find more shells would be an open and shut case of “Causing unnecessary suffering” in the UK.
My favorite response so far:
Not sure if this applies but, apparently chickens are not legally considered livestock under the law (and Cricket supposedly killed some chickens).
§ 780.328 Meaning of livestock.
The term “livestock” includes cattle, sheep, horses, goats, and other domestic animals ordinarily raised or used on the farm. This is further discussed in § 780.120. Turkeys or domesticated fowl are considered poultry and not livestock within the meaning of this exemption. - SOURCE
Just saying…I know this was way too long ago to be punished (legally) today.
Oh, OG, that’s funny!!
The most recent Trump campaign poster:
If the dog is healthy and happy it should not be killed, but surrendered.
I can imagine it would be the discretion of those bringing charges. (I realize it’s been awhile ago, but she’s bragging now)
Still it’s wrong. Immoral. Inhumane and disgusting.
My husband has hunting dogs. They are not pets. They have a very nice kennel and are fed well. Vet visits and pest control are always attended to.
If a particular animal doesn’t do his job he’s relieved of his duties. Kept for breeding or given to a person wanting a pet or a beagle for rabbits not deer.
It’s not hard to find people wanting pure bred dogs.
They are semi-valuable and he gets asked all the time if he has puppies.
Actually he’s out of the puppy business now. His kennel dogs are getting older and basically in their retirement home.
You don’t have to shoot them. Ever.
Ruthless! 
Buckshot for deer-hunting is only preferred in very specific situations - either close-in stalking, or trying to hit small deer on the run. Outside those situations it’s controversial and not recommended - shotgun slugs and rifle rounds are much more common.
This isn’t a soft-pedal, it’s the “look how much I triggered the libs” phase of this PR operation. It’s planned, it’s necessary, and it’s working.
For Republican info ops, you’re not the audience. You’re an instrument. Your reaction to this story, seeing it as stupid, enraging gaffe, isn’t some boneheaded misstep. It’s a required part of the formula!
Except for Old Yeller.
And Cujo.
I think your read of the situation is spot on. If you’re wrong, so am I.
Rabid and supernatural are different things.
I mean the Hound of the Baskervilles is not a house pet. 
Meh, her most recent Twitter post doesn’t really support a “look at all you triggered snowflakes!” narrative – which I imagine is where she was originally going with all this. Instead, she seems to be deliberately steering away from that take. Saying “I can understand why some people are upset” is not owning the libs. My interpretation is that she has belatedly come to recognize the killing a dog is not a political winner and she’d trying to put this in the rearview mirror as rapidly as she can.
YMMV.
Off topic, but: it’s legal to hunt deer with dogs where you live?
Yes. It is at certain times.
They are tracking dogs.
Pets or not, I bet your husband treats them kindly rather than abusing them; trains them to do their jobs without brutalizing them when they goof up; has a kind word and a pat on the head when they do well. Because that’s how you get good working dogs.
I bet the dogs get all happy and excited when they see him, and not just because he brings them food. He and they are pack.
You got it. Exactly.
It is highlighting the fact that she upset the libs, which is the most worthwhile part of this exercise. And the rest of the tweet is her springing the outrage trap to make the self-flattering points this was always intended to make:
She knew this anecdote would propel her onto a soapbox where she could crow about her own virtues while basking in the sheen of “libs hate me.” This isn’t some mastermind plan, it’s bog-standard reputation farming that’s been going on since George W. Bush moved to Texas and started talking like a cowpoke.