He studied at Oslo Music Conservatory, the forerunner of the Norwegian Academy of Music.
He was the father of canoer and mathematician Arne B. Sletsjøest From 1945 onwards, he was violist, later solo violist of the Oslo Philharmonic. He played in the orchestra until 1981, when he retired after 36 years of service.
In the former, the concert leader Henry Johnsrud was the leader, while Kåre Fuglesang led Den Norske Strykekvartett.
In this quartet, he played alongside the violinist Aage Wallin and cellist Arne Novang. After his retirement at age 65, he was a freelancer for the Norwegian National Opera for five years.
Sletsjøe was a member of the emsembles Johnsrudkvartetten (1948–1953) and Den Norske Strykekvartett (1954–1965).