This will mark all tickets in all departments closed.
UPDATE `support_tickets` SET `status` = 'closed'
Are you wanting to close them in a single department only? If so then you'll need to find the department ID in the 'support_departments' table and use the following. Where the number 1 is you'll need to change it to the department ID of choice:
UPDATE `support_tickets` SET `status` = 'closed' WHERE `department_id` = '1'