Updating workflows in Jira Service Desk without impacting previously closed tickets

You cannot delete a workflow if it is associated with a workflow scheme, so the first thing you would have to do is update the workflow scheme so that issue types using the workflow are associated with another workflow. 

If you publish a draft workflow in which you removed a status, you will be asked to map the deleted status to an existing one in the workflow. If your draft is only adding statuses, you are changing transitions, or making changes to conditions, validators, or post functions it will not affect existing issues since existing statuses are not changed.