Born in Düsseldorf, Eupen received a law degree before World War II similar to other notable members of the Nazi Party such as Hans Frank, head of the semi-colonial General Government. Eupen joined the Schutzstaffel with the card number 4528. After the invasion of Poland he was promoted to the position of Commandant of Treblinka I in the summer of 1941, ahead of the camp's official founding which took place in November 1941. He supervised the building of barracks as well as barbed wire fencing tall, around the perimeter. Treblinka I was a gravel quarry equipped with heavy machinery, essential to the production of concrete and road construction. Before the German occupation, the mega quarry was owned by the Polish industrialist Marian Łopuszyński who built a railway track connecting the mine with Małkinia–Sokołów Podlaski junction. Setting up a penal colony there was the idea of Sturmbannführer Ernst Gramss who first ran it as his own personal business venture in occupied Poland. The quarry became vital during the German attack on the Soviet Union, supplying gravel for the strategic road-building programme around the German–Soviet border.
Eupen was in charge of Treblinka I officially from 15 November 1941, until its closing on 23 July 1944. He worked closely with the SS and police commandanture in Warsaw during the deportation of Jews to the gas chambers of Treblinka II in early 1943, in order to have the slave labour brought to him from the Warsaw Ghetto for necessary replacements. He claimed to have been a German-Dutch aristocrat and liked to have his wife and two little sons visit him in occupied Poland. Eupen was feared even by his own SS subordinates penalized by being sent to the Eastern Front for even the smallest infractions. He arranged to have a garden built by his house with a pond and water fowl. Reportedly well-mannered, Eupen nevertheless had a reputation of a notorious sadist who often personally executed prisoners, "taking shots at them, as if they were partridges" wrote Franciszek Ząbecki, the Polish station master. Prisoners who worked 12- to 14-hour shifts received watery soup for breakfast, similar soup for lunch, and the roasted-grain beverage with rye bread for supper, each loaf shared by the 10 of them. During the liquidation of the camp, some 500–700 inmates were executed by the SS in the forest, and all structures were burned to the ground. Eupen's luck ended shortly thereafter. He was killed by Polish partisans near Jędrzejów in mid December 1944, ambushed on the road. He jumped out of the car and ran on foot as far as Lipówka village where he crawled under a pile of hay. The partisans machine-gunned his hiding place and learned who he was only from the documents they found on his corpse.
