what do you mean with task list? The "my tasks" webpart that shows you your tasks generated by workflows?
What information do you want to save or delete?
Do you have any screenshots?
On a SharePoint site you will likely find two task lists. Tasks, and Workflow Tasks. These lists are designed to handle tasks that are automatically generated by workflow actions like the "Flexi Task" for example. If you want to have a Task List for some other use I would create what you need and use a list name that is unique. I think you should leave the default lists to operate as they are designed. Now, if you want to use automation to access the task lists where you workflow tasks are generated, that can be done and is pretty straight forward. can you provide some clarification as to what you ant to do?