Maxwell was educated in the public schools and then at West Virginia University, graduating in 1900.
He opened a practice in Clarksburg, and was elected to the West Virginia House of Delegates in 1905 as a Republican.
In May 1909 he was appointed as judge of the criminal court in Harrison County, serving until 1912.
He was appointed to the West Virginia Supreme Court of Appeals on August 21, 1928, and elected on the Republican ticket to a full term in November of that year, serving until December 31, 1940.
His son Porter Wilson Maxwell commanded a squadron of Navy divebombers during World War II; he was killed in action on July 24, 1945.