Klemensiewicz was born in Kraków. His father, Robert, was a teacher of history and geography and a headmaster of a secondary school. From 1892 the family lived in Lwów, where he finished polish gymnasium, and in the years of 1904-1908 had been studing chemistry, physics, and mathematics at the Lwów University. In the years 1913 - 1914, he worked with Marie Curie in Paris. In 1920 - 1940, he was an ordinary professor of physics and electronics at the Lwów Polytechnic. In years 1940 to 1942, he was in Kazahstan (deported), then Iran, Egypt, and Great Britain (1944 till 1956). From 1956, he was a professor at the Silesian University of Technology in Gliwice.
Klemensiewicz was also an accomplished mountaineer and skier, author of the first Polish-language manual on mountain climbing (1913), co-founder and vice-president (1922–1939) of Polish Skiing Association (pl:Polski Związek Narciarski). He died, aged 76, in Gliwice.