Born in Saloniki, Ottoman Empire (now in Greece), Aslan lived in Vienna from 1897 until his death. In 1917 he joined the "Deutsche Volkstheater" in Vienna and was active at the Vienna Burgtheater from 1920–1958, where he mainly played classical heroes and complex characters such as Hamlet, Mephisto, Marquis Posa, and Nathan[disambiguation needed]. Aslan was the director of the Vienna Burgtheater from 1945-1948. In 1929 he was the first actor to be awarded the title "Kammerschauspieler".
Aslan once said to fellow actor Gustav Gründgens: "Mr. Gründgens, you're the greatest German actor, I am the greatest German actor. You're a homosexual, I am a homosexual. But one thing you should never forget: My family comes from Konstantinopel via Thessaloniki to Vienna. And you, Mr. Gründgens, you are from Dusseldorf."