Anthony Wood says that after taking his degrees he "applied himself to the study of politics and learning".
He wrote little, and injured his health by the "continued bibbing of strong and high-tasted liquors".
Wagstaffe died "in a manner distracted" at his lodgings in Holborn, opposite Chancery Lane, on 2 September 1677, and was buried in Guildhall Chapel.
Letters of administration were granted to his aunt (father's sister), Judith How, on 4 September 1677.
Wagstaffe published: He also contributed a Greek poem to Britannia Rediviva, Oxford, 1660.