One possible way is to look at the access logs, which provide the information regarding the action (which in this case delete), the username, and the date and time.
You will need to enable the access logs first, by 'Administration' > 'System' > 'Troubleshooting and Support' > 'Logging & Profiling' and click the 'Enable' link on 'HTTP Access Logging'. A new file will then be created (atlassian-jira-http-access.log) on the JIRAHOME/logs directory.
You can refer to the following doco for more info:
Hope this helps :)
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