Being asexual, sex-repulsed, but still having a libido is destroying my mental health. How can I get rid of my libido?

It sounds like you are going through a very conflicting time. I think a good place to start is to learn to accept your libido. Viewing it as a really bad thing and trying to get rid of it may add to the feeling of infliction, when having a libido is a normal brain response that cannot be easily subdued. I appreciate that you are asexual, but working out why you are sex-repulsed and working through that with a therapist may help you feel a bit more comfortable with experiencing a libido when it does happen. I know people can be sex-repulsed following trauma, so it may be a good time to start working through that trauma and allowing yourself to at least relieve yourself when you do experience a high libido (not meaning to have sex with someone else of course). Hope this helps.