Beard was born in Montville, Connecticut on May 8, 1839, to Rev. Spencer F. Beard, a Congregational minister, and Lucy A. Leonard. Beard's mother died in 1842 and his father remarried the following year to Mary Ann Fellowes. He graduated from Yale College in 1862, and received his medical degree from the College of Physicians and Surgeons of New York in 1866. While still in medical school during the American Civil War, he served as an assistant surgeon in the West Gulf squadron of the United States Navy aboard the gunboat New London. After the war and graduation from medical school, he married Elizabeth Ann Alden, of Westville, Connecticut, on December 25, 1866.