Instead of removing responses from a ticket to create a new ticket with it would be more beneficial to copy the content of the reply and create the new ticket from the copied content. Ideally you would be able to edit the content and subject of the new ticket before before it is created. This would also leave the original content in place in its original ticket.
It would also a log entry to the ticket stating the ticket was split and include the new tickets ticket id/number as part of the log entry. An inline ticket note would also be left stating the ticket was split and as part of the note it would include the new ticket number.
An example, if 5 replies into a ticket the customer submits 3 unrelated questions and one related question, the analyst can split this into 3 new tickets, each new ticket having one of the three original questions. This also allows there to be a history of the split out response in the original ticket and for better organization throughout all tickets (by limiting their scope to one unique problem/question /issue). The one related question also stays in the original ticket and the analyst can continue to provide assistance for that question without losing the question from being split into another ticket.