Clarence H. Dyer was born on July 21, 1832, in Connecticut to Thomas Dyer. His father was a Democratic politician who served as mayor of Chicago in the 1850s. The family moved to Chicago, Illinois, when Dyer was a child. By 1860, he was working as a railroad agent in Thornton, Illinois, and he owned $100 of personal property.
He enlisted in the Union army in 1861 and served as a captain and assistant adjutant general. He mustered out in 1866, and he later received a brevet promotion to major.
Dyer returned to Chicago after the war, and he married Esther E. Rutter. They had at least two children: George, born around 1871; and Thomas, born around 1873. He worked as a coal merchant, and he employed at least one white domestic servant. He died of heart disease in Woodstock, Vermont, on August 10, 1894.