He studied law in Keokuk and at a law school in Albany, New York and was admitted to the bar in 1858, commencing practice in Keokuk.
He was the uncle of Samuel B. Pettengill. He moved to Carson City, Nevada in 1861 and to Humboldt, Nevada in 1862 where he commenced practicing law. He was elected a Republican from the Montana Territory to the United States House of Representatives in 1870, serving from 1871 to 1873, being unsuccessful for reelection in 1872.
On December 18, 1871, at the urging of Ferdinand Vandeveer Hayden and after learning of the findings of the Hayden Geological Survey of 1871, Clagett introduced the Acting of Dedication bill into the House that ultimately led to the creation of Yellowstone National Park.
Clagett Butte in Yellowstone is named for his honor. Afterwards leaving Congress, Clagett resumed practicing law in Deer Lodge, Montana, Denver, Colorado, Deadwood, Dakota, Portland, Oregon and Coeur d"Alene, Idaho.
He was president of the Idaho constitutional convention in 1889 and was an unsuccessful candidate for the United States Senate from Idaho in 1891 and 1895. He moved to Spokane, Washington and resumed practicing law until his death there on August 3, 1901.
Clagett was interred in Greenwood Cemetery in Spokane.
Clagett was a member of the Nevada Territorial House of Representatives in 1862 and 1863, was a member of the Nevada Assembly in 1864 and 1865 and practiced law in Virginia City, Nevada, Helena, Montana and Deer Lodge, Montana.