Martin Anderson, of Grantsville, said he found the 10 Charlet cross beef cattle "strewn around" a popular climbing rock Friday. The animals were in fields where his family's herd has grazed for 50 years.
Six of the cows and the calf were shot dead; the three remaining cows had to be euthanized, Anderson said.
"The calves were all laying by their dead mothers - that's a sad sight to see," Anderson said.
The animals had bullet wounds in their heads, torsos, shoulders and hips, and many were shot multiple times, he said. When Anderson found them Friday evening, their injuries appeared to be a day or so old, he said.
The financial loss is $10,000 to $15,000, he estimated.
The Humane Society of Utah is offering a $3,000 reward for information leading to the conviction of the shooter.
"We're outraged someone would do this," said Humane Society director Gene Baierschmidt.