Your reminders and timers are stored in a file with the extension .duedb. It is a machine-readable JSON file, compressed with gzip.
To obtain a copy of this file, you can go to Due > Settings > Backup > Current > Email to email a copy of it to yourself.
You should then rename the file with the extension .json.gz, decompress the file using a gzip software (which is natively installed on Mac OS X) to obtain the file in JSON format.