Murphy attended the Hopkins School, graduating in 1895. He then went on to study at Yale University graduating in 1899 with a Bachelor of Fine Arts degree.
After a year spent at the Yale Graduate School preparing for a career as an architect, Murphy was first employed in this capacity in the New York offices of Tracey and Startwout in 1900. Together they took on work such as designing the early Loomis Chaffee campus in 1912, and successfully earned commissions to design numerous private residential and college academic buildings in the North East of the United States, in China and in Japan. Examples of their architectural work still extant include the historic administration buildings, old library and college chapel of Rikkyo University in Tokyo.
After Dana left in 1921, the firm continued as Murphy, McGill & Hamlin until 1924 when Murphy established his own independent practice.