DMS is right that there is a new capability of Event Manager that allows for a child incident to be attached or detached from the existing process. In short, you will need to create a web services enabled object that is pointing at the EM url as part of the source process that you are cloning from. You will then need to add that as a process step after the clone action and pass the ref number of the newly created process. This will invoke EM to carry out the detach action on that specific child process. Check out the new feature for 7.8 and also the main Event Manager documentation on creating a web services enabled object.
Andy