If you remove a mole by using acv does that kill the cancer cells as well?

Not likely: Apple cider vinegar has been discussed as a treatment for skin cancers, but is not standard; it has a low probability of working. A small amount of evidence suggests vinegar might kill cancer cells in a culture, but none to show that applying it to the skin kills the cells in a nevus (mole) or a skin cancer. If you have one or more moles you worry might be cancer, see a dermatologist.