Hopko was born in the Rusyn village of Hrabské, Austria-Hungary in county Šariš, presently in eastern Slovakia. His parents, Basil and Anna née Petrenko, were landless peasants. While Hopko was still an infant, his father was struck by lightning and died. His mother left him in care of her father, while she emigrated to the United States in search of work. When Hopko was 7 he was sent to live with his uncle Demeter Petrenko, a Greek Catholic priest.
He attended the Evangelical gymnasium in Prešov, then Czechoslovakia, graduating with honors in 1923. Hopko studied at the Eparchial Seminary in Prešov. He had dreams of joining his mother in America, and of pursuing his priestly vocation there, but the cost of recurring health problems left him unable to afford to travel. He later wrote that when he finally decided to stay and to serve in his homeland, he was suddenly cured, and realized he had been given a sign about his calling. He was ordained a Greek Catholic priest on 3 February 1929.
He served as a parish priest (1929–1936) at the Greek Catholic parish in Prague, the Czechoslovak capital, where he was known for his focus on the poor, the unemployed, and students. His mother returned from the US after 22 years and rejoined her son in Prague, becoming his housekeeper at the parish rectory.
In 1936 he returned to teach in Prešov's Eparchial Seminary, and was awarded the title of monsignor. He had already begun graduate studies at Charles University while in Prague, and he completed his Doctor of Theology in 1940 at Comenius University in Bratislava. In Prešov he headed the Eparchy's publishing division, where he edited a monthly periodical.
After World War II, a growing Soviet Bolshevik influence caused Bishop Pavol Peter Gojdič of Prešov to ask the Vatican for an Auxiliary Bishop to help defend the Greek Catholic Church. Hopko was appointed to the post on 11 May 1947. The Communist take-over of Czechoslovakia wreaked havoc on the Greek Catholic Church. In 1950 it was officially abolished, and its assets were turned over to the Russian Orthodox Church. Gojdič was arrested and was imprisoned for life. Hopko was arrested on 28 April 1950 and kept on starvation rations and tortured for weeks. Eventually he was tried and sentenced to 15 years for the "subversive activity" of staying loyal to Rome. He was repeatedly transferred from prison to prison. His health, physical and emotional, failed, and in 1964 he was transferred to an old age home. He never recovered his health.
During the Prague Spring the Czechoslovak government legally cleared Hopko on 13 June 1968 and the Prešov Eparchy was restored. However, activists insisted that a Slovak bishop be appointed to the see, and the Vatican named the Slovak priest Ján Hirka as Hopko's successor.
Hopko died at age 72 in 1976. On 14 September 2003 Pope John Paul II beatified him at a ceremony in Bratislava, Slovakia.