Even though it is not recommended that you delete the old incident calls and archive them instead, if you have to delete certain calls; the best way will be to do an advanced find from Incident ID1 to Incident IDn depending on your range, filter them on Status = Closed; and then delete them by a simple "Select All" and then "Delete" on the right click options pop-up. This can be done using the Administrator Access.
Hope this helps you...
Modesty is good!! But remember, all your life other people will try and take your achievements away from you, don't make it easy for them.
The old Incident from the Service desk can be removed by doing archiving or using the WEB-API. If you develop your own WEB-API application where you can set the filters as per your requirement, which in turn helps you to remove the Old & closed incidents from OVSD.
In SD, Archiving process is used to delete the entities. In admin console-system panel- archive settings. Each entity, servicecall, incidents, problem etc have a view called the Archive servicecall(table), archive incident(table). All these table views store the items that can be archived. By default you will see the filter of status=closed on these.
In the Archive settings, you will see 2 tabs, view and location, ideally if your entity has attachments then archive the attachments also. If you have servicecalls and incidents related to eachother and both are in closed status then when archiving you can choose the servicecalls and incidents views.
Initially you can go to incident entity and change the view to archive incident(table) view and check the incidents that are going to be archived.
Archiving process in SD is slow and gives performance hit to the application. So ideally it should be done off-peak time. During maintenance hours.
For your question of deleting incidents in one shot, archiving is the recommended way in SD.