To dispel is to get rid of something that's bothering or threatening you, regardless of whether that's warts, worries, or wild dogs.
The nifty thing about dispel is that you can use it when talking about emotional problems (such as worries and fears) as well as physical ones (such as wild dogs). Note, however, that when dispel is used in reference to physical foes, it often has the added meaning of scattering your opponents in all directions. So, while you can dispel a pack of wild dogs, you should just chase off or drive away a lone wolf. Good luck with that, by the way.