Polasek was apprenticed as a youth to a furniture maker in Vienna and came to the United States in 1901. Joining his brothers who had settled earlier in the midwest, he worked in several factories in Iowa and Wisconsin, carving altars for churches. Having been inspired by the work of Charles Grafly which he saw at the Saint Louis Exposition in 1904, he entered the Pennsylvania Academy to study with the master shortly thereafter. Beginning in 1907, he won the Cresson Fellowship for three years and was thereby afforded the possiblitiy of travel and study in Europe. His training continued at the American Academy in Rome where he was in residence until 1913. In that year, he exhibited The Sower at the Paris salon and was awarded an honorable mention. That full-length male nude was typical of his work from his Roman years.
Polasek's European experience was followed by three years in New York. Then, in 1916, he accepted a position at the Chicago Art Institute as chairperson of the sculpture department. As Beatrice Proske has pointed out, Pol sek's work from this period tended toward the idealized and included representations of both robust young men and beautiful young women. Examples include Fantasy (Metropolitan Museum of Art), modeled in Rome in 1913, Aspiration (Detroit Institute of Arts) which won the Widener Gold Medal at the Pennsylvania Academy in 1914, and Man Carving His Own Destiny (1920; Brookgreen Gardens and elsewhere) for which the sculptor used his own body as the model.
Several monumental commissions also came to Pol sek, works such as the bust of Daniel Boone for the New York University Hall of Fame; the Gov. Yates Memorial for the city of Springfield, Illinois; and a monument to President Wilson for the city of Prague (destroyed, World War II). He also modeled portrait busts of several artists, the best known being that of Charles Hawthorne for which Pol sek won the Logan Medal in 1916. During the late 1930s and early 1940s, he executed a number of religious works including several for the Cathedral of St. Cecilia in Omaha.
Polasek began exhibiting at the National Academy in the early 1920s and continued to do so for the rest of his life. He retired from teaching in the early 1940s and in 1950 moved to Winter Park, Florida, where he built a studio and worked for his remaining years. He married his former student and biographer Ruth Sherwood.