Tarsney was born in Ransom, Michigan and attended the common and high schools. He worked on the Government roads in Tennessee until the close of the Civil War. When he returned to Michigan, he settled in Saginaw, where he was employed as a sawmill engineer and became a marine engineer in 1867. He graduated from the law department of the University of Michigan at Ann Arbor in 1872 and was admitted to the bar the same year and commencing practice in East Saginaw.

He was elected justice of the peace in 1873 and city attorney from 1875 to 1878, when he resigned. His brother, John Charles Tarsney, was a U.S. Representative from Missouri. His sister Mary E. Tarsney married Thomas A. E. Weadock who became a U.S. Representative from Michigan after her death.

In 1880, Tarsney was an unsuccessful candidate for election to the 47th United States Congress, losing to Roswell G. Horr. He was a delegate at-large to the Democratic National Convention in 1884. That year, he defeated Horr to be elected as a Democrat from Michigan's 8th congressional district to the 49th Congress. He defeated Horr again to be re-elected to the 50th Congress, serving from March 4, 1885 to March 3, 1889. He was an unsuccessful candidate for re-election in 1888, losing to Aaron T. Bliss.

Tarsney moved to Detroit in 1893 and resumed the practice of law. He served on the corporation counsel of Detroit from 1900 to 1908.

The following year, he died at the age of sixty in Detroit and is interred in Calvary Cemetery in Saginaw, Michigan.

• United States Congress. "Timothy E. Tarsney (id: T000044)". Biographical Directory of the United States Congress.
• The Political Graveyard