Uritamm was a student of Artur Kapp at the Estonian Academy of Music and Theatre, graduating in 1937. He was on the faculty of the same school from 1940 until 1941, during which time he received a number of awards for his compositions. Tiring of the academic atmosphere and unable to find a position at the conservatories in Leningrad or Moscow, he resigned to work in a mill in Koluvere, managed by his brother. He was asked by Artur Kapp, then director of the Conservatory, to reconsider his decision, and he returned to his alma mater in 1945, staying until 1946 and teaching music theory. During the latter period he also served as the director of the Estonian Music Foundation and as the music editor of the newspaper Hammer and Sickle. He was ousted from his positions by the Soviets in 1946; he was also expelled from the Composers' Union for refusing to write music in the approved manner. From 1946 to 1947 he served as the organist at the Estonian Evangelical Lutheran Church of St. John in Kullamaa, following in the footsteps of Johannes Tobias, whose son Rudolf, considered the founder of Estonian classical music, also spent much time at the church. From 1950 to 1955 Uritamm taught music at a high school in Märjamaa, and from 1955 until 1961 he taught children at a school in Pärnu.
For political reasons, much of Uritamm's work remained unheard for long stretches during his career; since Estonia gained independence in 1991, however, his work has begun to appear on concert programs. His music has been described as ironic and deriving some of its sonic character from folk music. Little of his work has been recorded, but the piano trio Three Faces of the Homo Sovieticus, written in 1948 (premiered in 2012) was released on compact disc in 2014, and two of his songs were recorded by the baritone Tiit Kuusik in 1976.
- "Artur Uritamm – elulugu". opetaja.edu.ee. Retrieved 13 August 2015.
- "Järvi ärgitas Artur Uritamme oma loomingut salvestama". parnupostimees.ee. 27 November 2002. Retrieved 13 August 2015.
- "Kullamaa kogudus – Organistid". edicy.co. Retrieved 13 August 2015.
- "Veebipood. Variatio Delectat. Linernotes – Kammermuusikud". kammermuusikud.ee. Retrieved 13 August 2015.
- "Tiit Kuusik. Metsateel – Estonian Music Information Centre". emic.ee. Retrieved 13 August 2015.