Damsgaard graduated from Århus acting school in 1993, he has since appeared on small theaters around the country. He have had small parts in various TV series and movies.
His voice credits include Strings, Dragon Ball as Piccolo and Captain Gi'nyu, Curious George, Bunnytown and many others.
In 2000 he was hired for DR's kids show Bamses Billedebog for the lead part of the fullbody puppet Bamse, a role he would share with the actor Henrik Lykkegaard, for the recordings of new episodes. They would be the 4th and 5th actors that have been inside the puppet since the character first appeared in 1982.