In java it's a bit difficult to implement a deep object copy function. What steps you take to ensure the original object and the cloned one share no reference?
A safe way is to serialize the object, then deserialize. This ensures everything is a brand new reference.
Here's an article about how to do this efficiently.
Caveats: It's possible for classes to override serialization such that new instances are not created, e.g. for singletons. Also this of course doesn't work if your classes aren't Serializable.