Simonton was born in West Hanover, southern Pennsylvania, and spent his childhood on the family's estate, named Antigua. His parents were the doctor and politician William Simonton and Mrs. Martha Davis Snodgrass, daughter of James Snodgrass, a Presbyterian minister, who was the pastor of the local church. Ashbel was named after Ashbel Green, president of New Jersey College. He was one among nine brothers and sisters. The boys used to call themselves the "quinque fratres". One of his brothers, James Snodgrass Simonton, four years older than Ashbel, was also a missionary to Brazil, spending three years as a teacher in the city of Vassouras, in the state of Rio de Janeiro. One of his four sisters, Elizabeth Wiggins Simonton, also called Lille, married the Presbyterian minister and missionary Alexander Latimer Blackford, a colleague of Simonton in Brazil and the co-founder of the Igreja Presbiteriana do Brasil.
Conversion
In 1846, the family moved to Harrisburg, where Simonton finished high school. After graduating in New Jersey College, in 1852, he spent about a year and a half in Mississippi, working as a teacher for young boys. Disappointed with the lack of attention by the local authorities for teaching, Simonton went back to Pennsylvania and tried to become a lawyer, although by that time many people would advise him to become a minister, something to which his mother had consecrated him at his birth. In 1855 he had a deep religious experience during a revival and went to the Princeton Seminary. In his first term, he heard in the seminary's chapel a sermon by Dr. Charles Hodge, one of his teachers, which moved him to the missionary work in foreign lands. He was ordained in 1859 and arrived in Brazil on August 12, the same year.
Ministry
Soon after organizing the Presbyterian church in Brazil, Simonton spent his vacation in the United States, where he married Helen Murdoch, in Baltimore. They came back to Brazil in July 1863. In the next year they became parents to Helen Murdoch Simonton, Simonton’s only daughter. Besides the Presbyterian Church, Simonton created a newspaper, Imprensa Evangélica, along with a presbytery and a seminary.
Death
In 1867, feeling ill, Simonton went to São Paulo, where his sister and brother-in-law were raising his daughter. Simonton died on December 9, 1867, victim of a tropical disease named "febre biliosa".