Cope was born in Philadelphia to Quaker parents. At an early age he became interested in natural history, and in 1859 communicated a paper on the Salamandridae to the Academy of Natural Sciences at Philadelphia. He was educated partly in the University of Pennsylvania, and after further study and travel in Europe was in 1865 appointed curator to the Academy of Natural Sciences, a post which he held till 1873. From 1864 to 1867 he was professor of natural science in Haverford College, and in 1889 he was appointed professor of geology and paleontology by the University of Pennsylvania.
His speciality was the study of the American fossil vertebrata. From 1871 to 1877 he carried on explorations in the Cretaceous strata of Kansas, the Tertiary of Wyoming and Colorado; and in course of time he made known at least 1,000 species and many genera of extinct vertebrata new to science. Among these were some of the oldest known mammalia, obtained in New Mexico. He served on the U.S. Geological Survey in 1874 in New Mexico, in 1875 in Montana, and in 1877 in Oregon and Texas. He was also one of the editors of the American Naturalist. He died in Philadelphia.
Cope's competition with Othniel Charles Marsh for the discovery of new fossils became known as the Bone Wars.