This can be tested with Junit and spring-test, a Junit test class can be written that get's injected with an object from the layer at which your aspect is being applied and mock the layer beneath it.
Then call the object to which the aspect is applied and assert that the results are as expected.
This is an example of how to test if method security (applied via aspects) is working. The test confirms that an AccessDeniedException is thrown as expected, proving that the aspect is working.
Other aspects could be tested in a similar way using spring-test and mocks.