Dr. Blumer was born in England, the son of a physician. He received a classical education in England, Germany, and France, attended the University of Edinburgh as a medical student (1874–75), and returned there for post-graduate education (1884–85). He emigrated to the United States to study medicine, and in 1879 he graduated from the University of Pennsylvania.
In 1880, Dr. Blumer was appointed as an assistant physician at the Utica State Hospital for the Insane, and in 1886, he became the superintendent. He was also editor of the American Journal of Insanity (1886–1894).
In 1899, Dr. Blumer left Utica to become Superintendent of the Butler Hospital in Providence, R.I. There, he instituted training for nurses and physicians until he retired in 1921. He was a founding member of the Rhode Island and National Mental Hygiene Associations and remained active in civic affairs.
He received honorary degrees from Hamilton College (N.Y., 1930) and Brown University, and was made an honorary member of Phi Beta Kappa at Brown in 1930. The research laboratory at Utica State Hospital was dedicated to him. Dr. Blumer was President of the American Medico-Psychological Association (1902–03).