No, they cannot be permanently deleted through the Spiceworks GUI. HOWEVER, do a search for "delete tickets" when you're reading this message (see the top right corner for the search field) to find a link that will give you a work around. As long as you're comfortable editing a database manually and potentially voiding any and all warranties, expressed or implied, blah blah blah, with the use of Spiceworks, you can use the directions provided.
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