Lots of others have already advised you to rethink your code to make it more testable - good advice and usually simpler than what I'm about to suggest.
If you can't change the code to make it more testable, PowerMock: https://code.google.com/p/powermock/
PowerMock extends Mockito (so you don't have to learn a new mock framework), providing additional functionality. This includes the ability to have a constructor return a mock. Powerful, but a little complicated - so use it judiciously.
You use a different Mock runner. And you need to prepare the class that is going to invoke the constructor. (Note that this is a common gotcha - prepare the class that calls the constructor, not the constructed class)
@RunWith(PowerMockRunner.class)
@PrepareForTest({First.class})
Then in your test set-up, you can use the whenNew method to have the constructor return a mock
whenNew(Second.class).withAnyArguments().thenReturn(mock(Second.class));