Struve was a lawyer, journalist, and businessman who was prominent in political, economic, and social affairs in Seattle in the 1880s and 1890s. During his two terms as mayor, he oversaw more than $500,000 in public improvements, including the grading of streets. He also served as a regent of Washington University (predecessor of the University of Washington), was an organizer of the city's cable car system, helped write a new city charter in 1890, and was a charter member of the Rainier Club (a private club whose members included the wealthiest and most influential men in the city).
A German immigrant, Struve lived in California before moving to Vancouver, Washington, in 1859. He bought the Vancouver Chronicle that year but sold it a year later. He was elected district attorney in Clark County in 1862, and was re-elected for three additional terms. He resigned in 1869, when he was elected probate judge for the county.
In the 1860s and 1870s, Struve was involved in state politics, as a member of the state legislative assembly, the legislative council, and numerous legislative committees. He moved to Olympia in 1871. Late that year, President Ulysses Grant appointed him secretary of Washington Territory. He held that office until the end of Grant's administration in 1877.
Struve moved to Seattle in 1879 and established a private law practice with attorney John Leary. Among his more notable clients was the Northern Pacific Railroad Company. He was the chief litigator for the company in Washington state until 1883.
He was appointed a university regent shortly after moving to Seattle, and served as president of the board of regents for four terms. In 1884, he was elected director of the public schools, holding that position for three years. His business interests included the cablecar system in Seattle. He was a major stockholder in the company that built a line from the Madison Valley to downtown Seattle. He also invested in several insurance companies and banks, often serving as an officer as well as a stockholder.
Struve was one of only four men to serve two terms as mayor of Seattle in the years before 1890, when the city charter limited the terms of mayors and councilmen to one year. He died unexpectedly, after a short illness, while on a trip to New York in 1905.