My mother's fingers were amputated. She's diabetic. I'm her daughter but not her legal guardian. Can I sue on her behalf?

You potentially can hire an attorney on her behalf.  It may depend on your mother's mental state and if she can consent.  If she cannot cosent you may have to open up a guardianship to bring the claim.  Opeing up a guardianship or purpose of a lawsuit is not difficult unless other family members may disagree.