Boyce was born on June 16, 1858 in New Texas, Pennsylvania – now Plum Borough —to a Presbyterian farm couple, David and Margaret Jane Bratton Boyce. The Boyces had three children: William Dickson, Mary, and John. During his rural childhood, Boyce acquired a love for the outdoors. He began teaching school at the age of 16 and then worked briefly as a coal miner. He returned to teaching before joining his sister at Wooster Academy in Ohio, which—according to school records—he attended from 1880 to 1881. It is uncertain if he graduated or was expelled.