Conventional wisdom suggests it’s not politically smart to brag about killing puppies, but South Dakota Gov. Kristi Noem is challenging that theory.

In a new book, “No Going Back: The Truth on What’s Wrong with Politics and How We Move America Forward,” Noem reveals that she once killed a 14-month-old wirehaired pointer because she was “less than worthless” as a hunting dog.

Even stranger: She suggests her willingness to kill the animal is a political selling point since it shows she will do anything that needs to be done, no matter how “difficult, messy and ugly” it may be.

And it was definitely all three of those things based on an advance copy obtained by the Guardian.

Noem writes the dog, Cricket, had an “aggressive personality” and needed training before she could be used to hunt pheasant, per the Guardian’s review.

Although Noem thought taking Cricket hunting with older dogs would calm her down, she kept ruining things by “chasing all those birds and having the time of her life.”

An electronic collar also failed to bring Cricket under control — a fact that she said became woefully apparent after the hunt when Noem stopped to talk with a local family. Cricket managed to escape the truck and attack the family’s chickens, “crunching [each chicken] to death with one bite, then dropping it to attack another.”

Noem ended up paying the family for the chickens Cricket killed, and said the dog’s reaction throughout the incident was “the picture of pure joy.”

“I hated that dog,” Noem writes, per the Guardian. She calls Cricket “untrainable,” “dangerous to anyone she came in contact with” and “less than worthless … as a hunting dog.”

Noem writes she realized at that moment that she had to put Cricket down, and shot the animal in a gravel pit.

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

The hardest part, Noem writes, may have been when her kids came home from school and her daughter, Kennedy, asked, “Hey, where’s Cricket?”

Noem thought enough of the dog-killing anecdote to tweet it out to her followers, saying, “If you want more real, honest, and politically INcorrect stories that’ll have the media gasping....”

But plenty of other people were gasping at her, too.