Hans Alexander Mueller was born in Nordhausen, Germany on March 12, 1888 to Julius and Marie Mueller. He studied at the Academy of Visual Arts in Leipzig and then taught there. The printmaker Lynd Ward was his student in 1927.

Some time in the mid 1930s he emigrated from Germany to the United States and settled in Scarsdale, New York, where he worked as a freelance book illustrator and artist. The December 4, 1939 issue of Life Magazine included a profile of the German American artist Hans Alexander Mueller (1888-1962), who had just published, Woodcuts & Wood Engravings: How I Make Them. It was somewhat surprising and bold that a major magazine would be interested in highlighting a German born printmaker or a book on printing techniques in 1939, but it helped cement his reputation in the United States.

“There have been many books on woodcuts,” wrote Lynd Ward for the book jacket, “but this one is without equal in its intrinsic quality. The woodcut artist is peculiarly dependent on the printing process for the realization of his full intent, and probably nowhere else in the world could this book have been produced with the full measure of care and high standard of craftsmanship that it is receiving at the hands of Elmer Adler and the Pynson Printers.”

In the United Stated Mueller went on to illustrate a number of literary works including such classic novels as Stevenson's Treasure Island and Kidnapped, Don Quixote, by Cervantes, several works by Joseph Conrad and a series of novels by Knut Hamsen.

Hans Alexander Mueller died in Merryall, Connecticut on July 7, 1962.