He graduated from Troy Academy in 1853 and from Union College in 1856.
He went to teach at Fort Edward Institute in New York. He left in 1862, having become co-owner, vice principal, and professor of mathematics and Latin. He took over Troy Academy in 1862 and helped turn it into a well-known girls' school, Ripley Female College. In 1864 he opened a men's college, Poulteney Normal Institute. Knapp abandoned his career in education in 1866, when he suffered a crippling leg injury, and moved his family to Iowa to farm. The first winter blizzard killed all his sheep, and he was forced to abandon farming. He served as Methodist pastor in Vinton, then from 1869 to 1876 as superintendent of the State School for the Blind. In 1872 a second accident to the same leg miraculously cured the previous injury, and he returned to farming. Knapp became a leading pig breeder in Iowa; he founded the state breeders' association and also took over editorship of the Cedar Rapids Farmers' Journal. In 1879 Knapp accepted the chair of agriculture at Iowa State College. He used this position to agitate for a national program of practical and scientific education. In 1885 Knapp abruptly left Iowa to begin afresh in Louisiana. He worked on a huge land colonization scheme at Lake Charles, financed with British capital. He then went independent and in 1889 opened the Home Company, which was to develop half a million acres of Louisiana prairie for rice and sugar cultivation. He began another farm journal, ran a bank, and organized the rice growers. In 1898 the U. S. Department of Agriculture sent him to Japan to study rice cultivation. On his return he introduced Kiushi rice to Louisiana. In 1902 he became special agent for the Department of Agriculture, charged with promoting scientific farming in the South. He fought the boll weevil menace in 1904 by setting up demonstration farms, which showed farmers improved agricultural methods. Out of this experience grew the community demonstration farm technique, the county farm agent system, and the boys' and girls' farm clubs. Knapp was a bold lobbyist and wrote many Department of Agriculture pamphlets. The organization Knapp created was formalized and nationalized by the Smith-Lever Act (1914) as the Farmers Cooperative Work Division. Knapp died in Washington, D. C. , on April 1, 1911. In 1914 the Knapp School of Country Life was founded in his honor in Nashville, Tennessee.
He married immediately after graduation.