Dimitrios was born into a family of hagiographers. He settled in Athens in 1900 with his mother and older brother and, the following year, enrolled in the painting department of the Polytechnic, where Volanakis, Roilos, Iakovidis and Geraniotis taught. It was not until 1919, at the end of the First World War, that the artist went to Paris to study at the École Julienne and the École Générale de la Chaumière and to exhibit at the French Artists' Salon. He returned to Athens in 1923 and was appointed professor at the School of Fine Arts in 1928.

During his stay in Paris, Biskinis came into contact with the occult beliefs that dominated art circles. He turned to dreams and the subconscious world to enlighten and sanctify the inevitable reality of death. His students were Diamantis Diamantopoulos, Nikos Eggonopoulos, Asantour Baharian, Paris Prekas and Panagiotis Tetsis.

He was a friend of poet Kostis Palamas and illustrated many of his poetry collections.