Imagine following code:
List list = .....
List spy = spy(list);
doThrow(new NullpointerException()).when(spy).get(0);
doThrow(....)
Mockito.doThrow(new NullpointerException()).when(spy).get(0);
I think the problem here is that you are trying to do a partial mock and so you have to have the annotation on your test class:
@PrepareForTest(List.class)
This may or may not work. Looking at my code where I test exception handling, I always have done it on a fully-mocked object, not a partially mocked one. Also, I have made extensive use of PowerMockito when partial mocking, so it is possible that library will do what you need.