Not easily.
Do not delete issues. When you delete it is GONE. Hardly a week goes by without someone wanting to restore an issue. Deleting issues will come back and bite you when it is the most inconvenient. I suggest closing with a resolution value of Deleted anything you want to delete. I implement a special transition only the project lead can execute and it requires filling in a reason field from a select list (such as entered in error, OBE, Duplicate, Other) and explanation text.
Deleting issues destroys historical data. Missing issue numbers will eventually cause a question about what it was and why was it deleted even if it was done properly. Missing data always brings in the question of people hiding something that may have looked bad.
The only viable way to restore an issue is to create a new instance of JIRA and restore a backup that has the issues. Then export them to a csv file and import them to your production instance. You will lose the history.
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