In "The Birth-Mark” by Nathaniel Hawthorne, what does the birthmark symbolize and why is Alymer trying to remove it?

Georgiana's birthmark is repeatedly linked to human nature and the fact that we are imperfect and inevitably destined for decay and death. The mark is repeatedly described as being "crimson" in color, and it bears "not a little similarity to the human hand," though it is much smaller. The narrator even references jealous women who refer to Georgian's birthmark as a "bloody hand." Further, it is "deeply interwoven [...] with the texture and substance of her face." Some say that Georgiana is otherwise perfect but for this mark, and the narrator claims that

It was the fatal flaw of humanity which Nature [...] stamps ineffaceably on all her productions, either to imply that they are temporary and finite, or that their perfection must be wrought by toil and pain. The crimson hand expressed the ineludible gripe in which mortality clutches the highest and purest of earthly mould, degrading them into kindred with the lowest [...] like whom their visible frames return to dust.

Thus, natural things, such as people, are all going to pass away someday, and all are ultimately reduced to the same dust. Georgiana's birthmark is a symbol of her mortality. It is the color of blood (itself often synonymous with life), shaped like a hand (not, for example, a paw or claw or hoof), and is linked to her finite nature. Humans are not perfect and cannot live forever. It does not take long for the proud Aylmer, Georgiana's husband, to select "it as the symbol of his wife's liability to sin, sorrow, decay, and death [...]." He recognizes it not as a symbol of her human beauty and fragility but of her human nature to be imperfect and corruptible. He wants to remove it and to be the one to perfect Georgiana, saying,

I feel myself fully competent to render this dear cheek as faultless as its fellow; and then, most beloved, what will be my triumph when I shall have corrected what Nature left imperfect in her fairest work!

He feels, with his complete trust in science, that he can do a better job than Nature. Such a dream—to improve on what Nature has made—almost never works out in literature, and this story is no different. Symbolic of her mortality, when Georgiana's birthmark has been removed, she dies.