How is "The Birthmark" by Nathaniel Hawthorne autobiographical?
Well, Hawthorne didn't have a wife with a birthmark that he tried to remove, in the process killing her! Rather, to answer this question I think you need to look at how Hawthorne's life impacted his fiction generally, and especially the themes of this work. It appears that one approach to viewing the birthmark is to regard it as a symbol of sin, and the way that all of us, no matter how "perfect," have some stain of sin on our lives. This is what Aylmer finds so hard to accept, leading him to trying every recourse to removing the birthmark. However, it is highly significant that when he succeeds, Georgiana fades just as her mark fades, indicating that sinfulness and its stain on our lives is an essential part of the human condition, and that without it we are not equipped or able to live on earth.
Hawthorne's own life seemed to have been overshadowed by this truth. Although he had every reason for happiness - he was described as "unusually handsome," had a loving wife and was famous for his work, he became increasingly dissatisfied, remote and disappointing to his friends. It appears that the themes that he wrote about were based on similar discoveries about his own soul and being which he found difficult to accept, just like Aylmer in "The Birthmark," and these discoveries prevented him from enjoying what could have been a pleasurable life.