One of Donald Trump’s potential running mates is facing criticism for sharing a story in her memoir about how she killed her dog.

Kristi Noem, 52, the governor of South Dakota, wrote in her soon-to-be released memoir that the dog, Cricket, was “untrainable” and “dangerous”.

After deciding she needed to be put down, Ms Noem led the dog to a gravel pit and shot her.

“It was not a pleasant job,” she wrote. “But it had to be done.”

The memoir, titled No Going Back: The Truth on What’s Wrong with Politics and How We Move America Forward, is due for release on 7 May, though an excerpt was obtained by The Guardian.

The story was met with condemnation online.

The Democratic National Committee said: “If you want elected officials who don’t brag about brutally killing their pets… vote Democrat.”

Meghan McCain, the daughter of 2008 Republican presidential candidate John McCain, said: “You can recover from a lot of things in politics, change the narrative etc – but not from killing a dog.”

Ms Noem defended herself in a post on Twitter/X, saying: “We love animals, but tough decisions like this happen all the time on a farm.”

She promised more “real, honest, and politically incorrect stories” in her upcoming book.

Ms Noem, who dropped out of college at age 22 to run her family farm in South Dakota, wrote in the memoir of trying to teach Cricket, a 14-month old wirehaired pointer, how to behave by taking her on a pheasant hunt with some older dogs.

But attempts to discipline her, including using an electronic collar, failed, she said.

On the way home from the hunt, she stopped to talk to a local family when Cricket escaped and attacked their chickens, “grabbing one chicken at a time, crunching it to death with one bite”.

She said that the dog “whipped around to bite me” when she tried to bring it under control and that during the incident, Cricket was “the picture of pure joy”.

After apologising to the family for the dog’s behaviour, she said she realised it had to be put down.

“I hated that dog,” she said.

The situation made her realise “another unpleasant job needed to be done” that day – getting rid of a male goat her family owned.

The goat was “nasty and mean”, smelled “disgusting, musky, rancid”, and would chase her young children, knocking them down.

Ms Noem said she shot down the goat in the same manner as Cricket, though the goat survived the first bullet, forcing her to go back to her truck to retrieve another shell.

The school bus dropped her children off shortly afterwards.

Noticing that the dog was nowhere to be found, her daughter asked: “Hey, where’s Cricket?”

In the book excerpt, Ms Noem said that she shared the story to illustrate her willingness to do things that are “difficult, messy and ugly” both in politics and in life if necessary.

“I guess if I were a better politician, I wouldn’t tell the story here,” she said.

Mr Trump, the presumptive Republican nominee for president, has hinted that Ms Noem is on his list of potential running mates.

Ms Noem served as her state’s lone member in the House of Representatives for eight years before being elected its first female governor in 2018.