Ammon was the son of Nathan Cram Tenney and Olive Strong.

His mother, and then his father, joined the Mormon church in the early 1840s, when Ammon was very young.

The family had been living in Nauvoo, Illinois, but then moved to Lee County, Iowa, across the Mississippi river from Nauvoo, about 1844.

Ammon's family left with the main body of Mormons when they left Nauvoo to go to Winter Quarters (Florence), Nebraska in 1846. In 1848, the family left Winter Quarters and traveled by wagon train to Utah, where they settled in Cottonwood, Grand County, Utah. The family later lived in San Bernardino, California; southern Utah; and Arizona.

Ammon learned to speak Spanish in California and used that skill to act as a Mormon missionary and scout in the Southwest United States. He spent most of his life as a Mormon missionary in Arizona, New Mexico, and Mexico.

Ammon was a polygamist; by 1872 he had two wives. In 1884, he was arrested and convicted of polygamy; he was sentenced to 3 1/2 years in the Detroit House of Corrections. He had served over two years of his sentence when he was pardoned by President Cleveland.

In 1890, Ammon wanted to take a third polygamous wife; to do so he had to go to Mexico, because the Mormon church had promised the federal government they would not continue practicing polygamy, although they did to some extent. Polygamy was also illegal in Mexico, but the Mexican government did not spend much time proscecuting people who practiced it.

He married his third polygamous wife in 1890 in Mexico. He brought his other two families to Mexico at about the same time.

About 1892, his first wife, Anna, separated from him because of his abusive treatment of her and the children.

Anna and her children continued to live in Colonia Diaz, Mexico, while Ammon and his other two wives moved to Colonia Dublan and other places in Mexico. In 1912, Mexican revolutionaries drove all foreigners out of Mexico, including Ammon's families.

Ammon married:

(1) Anna Sariah Eagar November 9, 1867 in Salt Lake City, Utah. They had ten children together. She separated from him about 1892.

(2) Eliza Ann Udall on December 12, 1872 in Salt Lake City, Utah. They had two children together. She separated from him.

(3) Hettie Millicent Adams on March 24, 1890 in Colonia Diaz, Chihuahua, Mexico. They had ten children together. She separated from him before the 1912 Mexican revolution.

Ammon lived alone in El Paso, Texas and other locations in the South and Southwest, until he died in Thatcher, Arizona.