Ms. Noem, a Republican who is widely seen as a contender to be former President Donald J. Trump’s running mate, shared details about shooting the 14-month-old dog, a female wirehaired pointer named Cricket, and an unnamed goat, according to excerpts first reported by The Guardian.

An avid hunter, Ms. Noem wrote that she had hoped to train Cricket to hunt pheasant, but that she proved “untrainable,” “dangerous to anyone she came in contact with” and “less than worthless” as a hunting dog. “I hated that dog,” Ms. Noem wrote, according to The Guardian.

It was after Cricket ruined a hunting trip, killed another family’s chickens and bit the governor that Ms. Noem recalled deciding to kill the dog; she shot Cricket in a gravel pit.

That was not the only blood Ms. Noem drew that day: She also shot a male goat that she called “nasty and mean.” Shot him twice, in fact: The goat jumped as she shot him the first time, according to The Guardian’s recounting of the book, so she fetched another shell and shot him again.

The whole ordeal was reportedly witnessed by a construction crew nearby. Ms. Noem wrote that as the workers returned to their jobs, a school bus came by to drop off her children.