You can do it the same way you do it with Mockito on real instances. For example you can chain stubs, the following line will make the first call do nothing, then second and future call to getResources
will throw the exception :
// the stub of the static method
doNothing().doThrow(Exception.class).when(StaticResource.class);
StaticResource.getResource("string");
// the use of the mocked static code
StaticResource.getResource("string"); // do nothing
StaticResource.getResource("string"); // throw Exception
Thanks to a remark of Matt Lachman, note that if the default answer is not changed at mock creation time, the mock will do nothing by default. Hence writing the following code is equivalent to not writing it.
doNothing().doThrow(Exception.class).when(StaticResource.class);
StaticResource.getResource("string");
Though that being said, it can be interesting for colleagues that will read the test that you expect nothing for this particular code. Of course this can be adapted depending on how is perceived understandability of the test.
By the way, in my humble opinion you should avoid mocking static code if your crafting new code. At Mockito we think it's usually a hint to bad design, it might lead to poorly maintainable code. Though existing legacy code is yet another story.
Generally speaking if you need to mock private or static method, then this method does too much and should be externalized in an object that will be injected in the tested object.
Hope that helps.
Regards