John Stanley Ortmann was having a routine day when he got the call: A mountain lion that had killed a sheep had possibly been shot and was hiding out in a brushy area near a busy road.

Armed with catch poles, a syringe with a euthanasia drug, and carrying a .40-caliber semiautomatic pistol, he located the mountain lion but had to crawl into the brush to catch him.

That's when the mountain lion surged into an opening in the brush, forcing Ortmann to his back. He had just enough time to draw his pistol and fire two shots. The mountain lion landed on top of...