He received a classical education and was graduated from Trinity University, Dublin, Ireland.
Beirne immigrated to the United States in 1793 and settled in Union, Monroe County, Virginia (now West Virginia). He engaged in mercantile and agricultural pursuits. During the War of 1812 he served as captain of a rifle company and as colonel of the Monroe County Militia.
He was elected as a Democrat to the Twenty-fifth and Twenty-sixth Congresses (March 4, 1837 – March 3, 1841).
Beirne was not a candidate for reelection in 1840 to the Twenty-seventh Congress and resumed his former business activities. Beirne died while on a visit in Gainesville, Sumter County, Alabama, March 16, 1845, with interment in the family burying ground at Union, Monroe County, Virginia.
His home at Union, known as "Walnut Grove," was listed on the National Register of Historic Places in 1977.
Beirne was a member of the State house of delegates in 1807 and 1808. Beirne was delegate to the Virginia constitutional convention in 1829 and 1830 and member of the State senate 1831-1836.