Mrsic was born in the Rasavci village near Prijedor, SR Bosnia and Herzegovina, Yugoslavia, to father Momir and mother Radojka. His father got a job in Sweden in the late 1960s. Dragomir moved with his mother and two older siblings to Sweden aged a month-and-a-half, and was brought up in Fittja, a suburb of southern Stockholm. His father worked as a chef at Grand Hôtel in the city, his mother as a cleaner at the local school. His father was a functioning alcoholic. At 14 years of age he witnessed his brother's friend's suicide jump. His two siblings, sister Ranka and brother Radomir "Rajko", died of drugs use.