You can't easily. I can think of two ways you can do this and neither are supported out of the box by Mockito or jUnit as far as I'm aware:
1) Byte code manipulation using cglib or similar library which would be moderately difficult to do and likely pretty fragile.
2) Alternate classloader. You can build a classloader that looks for an attempt to load the OtherObject class and replaces it with an anonymous OtherObject class that gives you the mocking behavior that you are looking for.
Most of the time you should be treating it as a dependency though. If you want to test opening a file, you probably actually want to test with a file so using the concrete class is probably fine. If you want to test a method's behavior that has opening a file as a part of it's logic, you could easily move that out to a dependency and then mock it out. In fact, that usually makes sense because what you store in a file one day, may need to be stored in a database another or be pulled down from the cloud on a third day, so segregating the logic around what you do with the file from the actual process of opening a retrieving the contents is often a logical separation of concerns anyway.