If I am right, there is currently no way of doing this using the UI.
So I suggest backing up the whole database and the osticket install folder on the webserver and search (Google, Bing, etc.) for how you can delete data inside a mysql database. Next you should delete the ickets inside the database.
But before you now start I hope you know what you are doing and in case something goes wrong just restore the backup ;)
Btw. That would be a great thing for a "Cleanup plugin" (delete every ticket older than x days etc.) ... will suggest that in the suggestions forum.