Maybe at first you think about why you should have all your messages deleted on Twitter. At first, I can't think of any field of application. But TwitWipe offers us to use this service for free and gives and even a few reasons why you should use this service. For example, if you give someone else's Twitter account or if you want to make a complete reboot. I don't need it, but if it's interesting for someone, you can use it without a great registration.
You can log in directly with your Twitter account and then (as I understood it) all messages can be deleted under this Twitter account at the touch of a button. This is not a service that runs to the server in the background, but you have to leave the twitWipe page open. This is the only way a script (Java?) runs and does the job. According to the programmer, many messages can take a whole night. If you need such a service, you can use it for free. However, I must honestly say that few will need such a thing.