You will need to delete the data in chunks. The following will delete the oldest logs in blocks of 1000. You may be able to increase the limit so that more logs can be deleted per run, but this all depends on your MySQL server performance. Remember to change the table name prefix to whatever you have setup in wp_config.php.
Remember to backup your database first!
DELETE FROM wp_posts WHERE post_type = 'dedo_log' ORDER BY post_date ASC LIMIT 1000
You may also want to remove log meta data from the postmeta table:
DELETE FROM wp_postmeta WHERE meta_key = '_dedo_log_download' OR meta_key = '_dedo_log_ip' ORDER BY meta_id ASC LIMIT 1000
Automatic purging of old logs will be implemented in an upcoming update, but until then you may wish to run the delete commands on a regular basis.