Jaroslav Řezáč played various sports in his youth in Bohemia. In addition to ice hockey he played bandy and rowed competitively for CSK Vysehrad. In World War I he served in Eastern Slovakia, and he was one of the founders of the first hockey club in Košice. He was already 36-years-old when he débuted in goal for the national team at the 1922 European Championships. In the decisive game against Sweden, Řezáč replaced the goaltender, helping the team win the title. Subsequently he participated as a reserve goalie in major tournaments and additionally acted as the manager of the delegation.
Řezáč played at the 1924 Olympic Winter Games, where he was also the Czechoslovakian flagbearer during the Opening Ceremony. Four years later he was again a member of the team but did not play. His last appearances as a reserve player and an assistant coach came at the 1929 European Championships, which Czechoslovakia won, and the 1931 World Championships. At home, he played for Česka Sportovni Spolecnost (ČSS – 1909-12) and later for Sparta Praha. Řezáč was later a coach and referee and represented Czechoslovakia on the International Ice Hockey Federation from 1923-46. In this position he was instrumental in bringing the 1925 European Championships to Czechoslovakia. Řezáč was a doctor of law.