Kiisk was born and raised in Viru County. In 1944, aged 18, he served in the anti-aircraft unit of the 20th Waffen Grenadier Division of the SS (1st Estonian), and took part in the Battle of Tannenberg Line. After World War II, he managed to obscure his military service from the Soviet occupiers. In 1946, he graduated from the Rakvere 1st Secondary School and enrolled at the Tallinn University of Technology. He switched the next year to the ESSR State Theatre Institute and in 1948, to the Russian Academy of Theatre Arts. Graduating in 1953, he returned to Estonia and joined the Estonian Drama Theatre.