There's indeed no method to deep copy as far as I know. One solution is to add all the axioms present in your first ontology to a newly created ontology instance. This way you keep everything in memory and no needs to re-read the files. The OWL entities (classes, properties, etc...) should be copied too.
The following code should work (not tested):
manager.addAxioms(newOntology, oldOntology.getAxioms());