Yes, this is quite commonly done as part of an LDSD implementation. If you look at the way the action 'Add Affected User' works in the OOTB incident workflow, that should give you the basic method.
You would expand the data collected by your Clone action to include more than just that collected by add affected user, but the same method applies. Collect the data, use the automatic action Create Incident to create a child and copy through all the data you want using Value Type. This child process will then have a life of it's own.