Joshua Squire "Squire" Hyde was born on April 10, 1849, to Squire Hyde and Eliza Ann Milloy, who were married on December 25, 1842, in Union County, Arkansas. By 1860, Squire resided in Claiborne Parish, Louisiana, with his mother and stepfather, Alexander Mashaw. When the Civil War began, Squire's brother, William, joined the Confederate Army; Squire never heard from or saw his brother again. In 1874, Squire Hyde married Nannie Permelia Lee. They originally resided in Homer, Louisiana, and were the parents of twelve children: Bertha Ann, William Lee, James Dorsey, Joshua Ellis, Mattie Alice (Wattis), Thomas Gordy, Frank Abner, Fernando Guy, Nannie Mac (Hudgens), Vera Vesta (Miner), Nellie Omega, and Lillian (McAlpin McKay). By 1900, the Hyde family lived in Webster Parish, Louisiana, and in 1901 Nannie died of malaria. Squire remarried to Sarah Jane "Sallie" Mitchell Miner in about 1903, and together they had one daughter, Willie Estelle Hyde.

Squire was a carpenter by trade. His work included remodeling the Claiborne Parish Courthouse in Homer, building coffins for paupers, and maintaining the area poor house. He was also known to make remedies for the ill in his community. In 1872, Squire joined Homer Lodge No. 152 and rose to rank of Senior Warden. Later, he was Worshipful Master of Dorcheat Lodge No. 276.

Due to the impact that malaria had on the Hyde family, a doctor advised Squire to relocate his family. The Hydes left Louisiana and settled in Lamartine, Columbia County, Arkansas in about 1907. Several years after the family's relocation to Arkansas, Squire contracted throat cancer. He sought treatment in Chicago but was unable to procure any help. Joshua Squire Hyde passed away on April 26, 1916, at the age of 67 and was buried in the Shiloh Lamartine Cemetery.