If my girlfriend went to an abortion clinic to get the procedure done but all of the fetus was not removed, can I sue the clinic for malpractice or at least get my money back?

First, if there is a worthwhile cause of action, it's your girlfriend--not you--who could sue; she is the person who was injured, and being her boyfriend does not give you any legal standing or relationship to bring s lawsuit on her behalf. ("Girlfriend" is not a legally recognized relationship, like "wife" is.)

Second, she may have a cause of action, in the sense of there being liability: if the clinic were, as it may well have been, negligent, or careless, in not removing all the fetus, they would have been at fault. However, even if there is liability or fault, it might not be a worthwhile case: in a malpractice case, all you can recover is your out-of-pocket medical costs, lost wages (if any), other direct out-of-pocket costs, and--for conditions causing long lasting or permanent impairment, disability, or disfigurement, some amount of "pain and suffering" compensation. However, if your girlfried suffered for a few days before going the emergency room and having the problem rectified, she would not be entitled to much if any pain and suffering award, so likely, all she could recover is her own out-of-pocket emergency room costs. But to the get them, if the clinic doesn't want to voluntarily pay her, she'd have to sue; and to bring a malpractice suit, you *must* hire a medical expert, which is expensive. She could spend more on the lawsuit than she would get back.