Ziniuk apparently told police that the horse had to be put down after being attacked by dogs. He faces felony charges of animal cruelty.
Riverside County Animal Services Department spokesman John Welsh described the animal as a roughly 1,000-pound white-grayish mare.
Animal Services Department Cmdr. Rita Gutierrez said the horse did not appear to have received proper veterinary care prior to its death.
Phillip Thomas, who lives in a trailer on Ziniuk's sprawling property and helps him with chores, said the horse had been suffering and Ziniuk was trying to put it out of its misery.
The horse was given hay after not having been fed for days and collapsed after overeating, Thomas said.
Thomas saw Ziniuk struggle under the weight of a sledgehammer as he clumsily battered the animal's head.
"Jack was trying to hit the horse over the head with the sledgehammer, but he did not have the strength to do this," Thomas said. "I could see the horse's tail. It was just flapping up and down."
Ziniuk eventually gave up and asked another tenant on his property to fetch a chain saw "to sever its head while it was still alive," Thomas said.
Thomas said he was leaving the property to go grocery shopping when he heard the chain saw roar to life behind him.
Ziniuk apparently called the sheriff's and animal control departments after the animal's head had been sawed off, Thomas said.
"I don't know what he was thinking really to call animal control," he said. "But he's a little out of his mind some of the time."
Ziniuk has been cited several times for having more dogs on his property than allowed without a kennel permit, among other offenses, Welsh said.
Ziniuk has at least 33 dogs and 10 goats, as well as peacocks and geese, he said.
"We've been down there at this particular property on many occasions," Welsh said. "He has a lot of administrative and criminal situations for failing to do a number of things."
Thomas said Ziniuk depends on his disability income from a heart condition and often has trouble providing for his menagerie.
"These animals are not necessarily fed the month through," he said.
The Associated Press contributed to this story.
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