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Clingerman was born Mildred McElroy in Allen, Oklahoma and her family moved to Tucson, Arizona in 1929. She graduated from Tucson High School and attended the University of Arizona. She married Stuart Clingerman in 1937.
Most of her short stories were published in the 1950s in The Magazine of Fantasy and Science Fiction, edited by Anthony Boucher. Boucher included her story "The Wild Wood" in the seventh volume (1958) of The Best from Fantasy and Science Fiction and dedicated the book to her, calling her the "most serendipitous of discoveries.":252–3 Her science fiction was collected as A Cupful of Space in 1961. She also published in mainstream magazines like Good Housekeeping and Collier's. Her story "The Little Witch of Elm Street" appeared in Woman's Home Companion in 1956.:374