However, if you wish to permanently delete all tickets, then you can do so by action called purge. First go to Tickets > All filter, where you modify the Custom filter to show all tickets, even the ones with 'spam' and 'deleted' statuses
Then you check in the checkbox that selects all tickets and the Mass action button will show up
In that "Mass action" window in the very first drop-down menu you choose "delete ticket", then "Add action" and in the second action choose "purge ticket". Then you can click "Run now".
The reason is that the "purge" action can only be executed on a deleted or spam ticket to prevent accidental purging of important data.
If you choose "Run in background", then the tickets will be deleted at the next run(s) of cron job and you can continue working in LiveAgent.
NOTE: If you once purge all tickets, there is NO WAY to bring them back, unless you have a backup of your database.