Mueller was born in Nordhausen in 1888. He studied in Leipzig and then taught there (Lynd Ward being a student). Before 1939 he emigarted to America where he undertook several ambitious illustrative projects, Kidnapped and Treasure Island, Don Quixote and to a series of novels by Knut Hamsen.

His standard manual of the medium (Wood Cuts and Wood Engraving) has a characteristic quote on the reverse of the jacket. "I love the woodcut as a form of artistic expression because it requires the simplest materials and comparative muscular strength. I love to exploit the full use of my five senses when wood, metal, paper, and color come within my grasp."