Henry Clay Drexler was born in Braddock, Pennsylvania, on August 7, 1901. He attended both Culver Military Academy and the United States Naval Academy, graduating from the latter in June 1924.
On October 20, 1924 Ensign Drexler was conducting drills aboard the USS Trenton (CL-11). Powder bags in her forward turret exploded, killing several men instantly. Ensign Drexler attempted to neutralize the remaining charge by dumping it into the immersion tank, but it detonated before he could reach the tank. He died as a result of his injuries while attempting to save the lives of his shipmates.