Growing up was no different than it was for most children in the Faroes at the time, and he was engaged in odd jobs while not attending school.

He studied under Jacob Jacobsen from Tórshavn, and he was a member of the first graduating class of the Faroese Teachers School (Faroese: Føroya Læraraskúli), after having also spent an academic year at a folk high school in Denmark.

During the 1896/97 academic year he attended Askov Folk High School, where he made the acquaintance of his compatriot Símun av Skarði.

Rasmussen also attended the State Teachers School (Danish: Statens Lærerhøjskole) in Copenhagen, where his main study area was science.

His teacher's position there was the source of his Faroese epithet Rasmus á Háskúlanum (literally, 'Rasmus at the high school').