After studying in Berlin with Carl Liebermann, he received his Ph.D at the University of Göttingen. Giesel worked at the Chininfabrik Braunschweig. Besides his work in the factory, Giesel's focus was on radiochemistry. Shortly after publication of the discovery of polonium in the summer of 1898, he started to isolate the new element from the waste of uranium production in the chemical plant E. de Haën in Hanover. By March 1899 he could present the first radium to the chemical society of Braunschweig and by mid-1899 he published his results on radium. Giesel improved the separation of radium from barium by using the bromides instead of the chlorides for the fractional crystallization. He produced large quantities of pure radium and polonium for commercial applications from uranium ore. Even William Ramsay and Frederick Soddy were buying radium from the factory of Giesel.
The use of Sidots blende (zinc sulfide) instead of barium platinocyanide as a luminescence material to make the radioactive rays visible was a commonly accepted improvement. He did several self-experiments with radioactive substances and was able to affirm the damaging effects of radioactive radiation on skin. Because of prolonged contact with radioactive material, fingers of his right hand had to be amputated and he suffered from lung cancer. He died of lung cancer in 1927. His name was included on the Monument to the X-ray and Radium Martyrs of All Nations' erected in Hamburg, Germany in 1936.