Edd was born on July 3, 1877 to Benjamin Ruff Grinstead and Kate Amanda (nee Rugh) on a family farm near Azen in Scotland County Missouri.

He was a graduate of West Point. By 1910 he was in Phoenix Arizona. He worked at the Indian School located there. He served in France during WW I where he commanded a battalian of Native American troops.

He died on September 30, 1924 as the result of an accidental gunshot wound self-inflicted in his back yard. He was buried at a cemetery in Phoenix Arizona.