He attended Quaker schools and was admitted to the bar in Bucks County, Pennsylvania, in April 1850.

He was appointed by Pennsylvania Governor John W. Geary to the Common Pleas bench in 1869 to replace F. Carroll Brewster, who had resigned to become Pennsylvania Attorney General.

[1][2] In 1874, Paxson was elected to the Supreme Court of Pennsylvania, assuming office as an associate justice in January 1875.

He stepped down from the bench in February 1893 to become a receiver of the Philadelphia and Reading Railroad Company.

[1][2] Paxson was married twice, to Mary C. Newlin from 1846 to her death in 1885, and to Mary Martha S. Bridges, widow of Samuel Augustus Bridges.