He was the son of Francis Savage of Dobs Hill in the parish of Eldersfield or Eldsfield, Worcestershire.
He entered as a commoner of Balliol in 1621 at the age of seventeen, but did not matriculate till 11 March 1625.
Savage submitted to the parliamentary visitors of the University of Oxford; and was presented to the rectory and vicarage of Sherborne St. John, Hampshire, in 1648.
He was recalled to Oxford by his election, on 20 February 1651, to succeed George Bradshaw as master of Balliol, then one of the poorest and smallest colleges, and proceeded to the degree of D.D.
on 16 October following; his dissertations on infant baptism were published in 1653, and provoked an answer from John Tombes of Magdalen Hall, to which Savage replied in 1655.