South Dakota Gov. Kristi Noem is trying to dismiss outrage over her confession that she shot dead a dog she “hated” as “fake news” — while doubling down on her “hard decision” to kill it.

The 52-year-old Republican attacked reports about the killing — which The Post revealed has destroyed her chances of being picked as Donald Trump’s running mate — even though they were based entirely on her own words from an upcoming memoir.

“You know how the fake news works,” Noem told Fox News, while not denying the accuracy of the leaked excerpts.

“They leave out some or most of the facts of a story, they put the worst spin on it. And that’s what’s happened in this case,” she said of her revelation that she shot and killed the 14-month-old wirehair pointer she “hated” and found “worthless.”

“I hope people really do buy this book and they find out the truth of the story because the truth of the story is that this was a working dog and it was not a puppy,” she said of Cricket, whom she said was just 14 months old.

“It was a dog that was extremely dangerous.”

“Noem claimed that Cricket “had come to us from a family who had found her way too aggressive.

“We were her second chance. And she was — the day she was put down was a day that she massacred livestock that were part of our neighbors,” she told Fox News.

“She attacked me. And it was a hard decision.”

Noem added that she had to make a choice between “keeping my small children and other people safe, or a dangerous animal, and I chose the safety of my children.”

“Farmers and ranchers, they expect it,” she continued.

“They know that once an animal like this starts killing, and starts killing just because they enjoy it, that is a very dangerous animal.”

The revelation has also drawn both outrage and mockery from Democrats and Republicans.

“They know that once an animal like this starts killing, and starts killing just because they enjoy it, that is a very dangerous animal.”

Several critics have compared the executions to an incident involving Sen. Mitt Romney’s (R-Utah) during his 2012 presidential campaign, over a story about him tying his dog to the roof of his car on a family road trip.

But Noem has repeatedly doubled down on her decision to kill her pet despite it having potentially harmed her chances in the GOP’s vice presidential nominee race.

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On Sunday, she continued to insist that her dog needed to be killed, on social platform X.