Restore a deleted mailing?
Two answers:

Do you have detailed logging eanabled?  If no, then no - you can restore a backup of your database (to a test site) and copy the data out.

If you have advanced logging enabled: you can use SQL.  You need to know the ID of the deleted mailing - you can check the titles with SELECT DISTINCT id, name FROM log_civicrm_mailing.  

Once you find the ID number, substitute the X at the end of this query for the ID.



INSERT INTO civicrm_mailing (id, domain_id, header_id, footer_id, reply_id, unsubscribe_id, resubscribe_id, optout_id, name, mailing_type, from_name, from_email, replyto_email, subject, body_text, body_html, url_tracking, forward_replies, auto_responder, open_tracking, is_completed, msg_template_id, override_verp, created_id, created_date, scheduled_id, scheduled_date, approver_id, approval_date, approval_status_id, approval_note, is_archived, visibility, campaign_id, dedupe_email, sms_provider_id, hash, location_type_id, email_selection_method, language, template_type, template_options, modified_date) SELECT id, domain_id, header_id, footer_id, reply_id, unsubscribe_id, resubscribe_id, optout_id, name, mailing_type, from_name, from_email, replyto_email, subject, body_text, body_html, url_tracking, forward_replies, auto_responder, open_tracking, is_completed, msg_template_id, override_verp, created_id, created_date, scheduled_id, scheduled_date, approver_id, approval_date, approval_status_id, approval_note, is_archived, visibility, campaign_id, dedupe_email, sms_provider_id, hash, location_type_id, email_selection_method, language, template_type, template_options, modified_date 
FROM log_civicrm_mailing WHERE log_action = 'Delete' AND id = X;