Finnerty was born in Loughrea, the son of a town trader. He moved to Dublin where he became a printer, later publishing The Press, a nationalist paper begun in September 1797 by Arthur O'Connor. Finnerty was closely associated with James MacHugo and Francis Dillon, fellow natives of Loughrea who built the local branch of the United Irishmen. A prosecution by the government against The Press in 1797 resulted in Finnerty being tried for seditious libel: the charge arose from his paper's strong criticism of the judges who sentenced William Orr to death and the Lord Lieutenant, who refused to reprieve him., Despite being defended by John Philpot Curran, he was found guilty in spring 1798 and sentenced to two years in prison. Despite this, he remained in correspondence with MacHugo.
On his release, Finnerty emigrated to London, working as a parliamentary reporter with the Morning Chronicle. In 1811 he was sentenced to eighteen months for libel against Lord Castlereagh. He died in Westminster in 1822.
Finnerty was supported by Percy Bysshe Shelley in A Poetical Essay on the Existing State of Things, a recently discovered text written at Oxford in 1811. The poem's 'hero' is Sir Francis Burdett, a figurehead for the campaign to support Finnerty, its targets are variously: Lord Castlereagh, the 'cold advisers of yet colder kings' who sent English soldiers to die in the Low Countries, and Napoleon, 'like a meteor on the midnight blast'.
- Case of Peter Finnerty, including a full report of all the proceedings which took place in the Court of Kings Bench upon the subject ..., London, 1811
- Galway Authors, Helen Mahar, 1976
- The District of Loughrea: Vol. I History 1791-1918, pp. 19–25,37 ISBN 0-9546567-0-9