He attended the public schools and St. Francis Xavier College, and graduated from Mount St. Mary's College with a Bachelor of Arts degree in 1876 and a Master of Arts in 1878.

He studied law, was admitted to the bar in 1878 and commenced practice in New York City.

Dunphy was later employed in the legal department of the New York Central Railroad.

In his final term, he was chairman of the Committee on Expenditures in the Department of Justice.

He was not a candidate for reelection in 1894 and resumed the practice of law in New York City.