Ševčík participated in the Czechoslovak Legion during World War I. After the war he studied law and from 1926 to 1934 represented the Slovak People's Party (incl. as secretary of the faction). After that, he worked in the agrarian sector.
From 1939 to 1942 he was the head of the YMCA administration in Bratislava.
Ševčík was an opponent of fascism and therefore joined the Slovak résistance movement. The Slovak résistance opposed the nominally independent Slovak republic that was established in 1939 by monseigneur Jozef Tiso but to a large extent controlled by Germans. In 1944 the Slovak National Uprising took place, in which Ševčík participated. The résistance forces met an early success in fighting with Slovak fascists and German troops, but later had to retreat.
In 1952 Ševčík was arrested and accused of opposition to the socialist development of Czechoslovakia.[1] He was sentenced to 17 years imprisonment,[1] but was released in 1960.
On 6 March 1965 Ševčík died. He was rehabilitated soon after.