Patrick, a Shopify Guru here :).
At the moment, there isn't a way to completely remove the old data from the store and start fresh. You can delete any test orders you've made from inside the admin but the counter will continue from the last order that went through. We may add this feature in the future for situations like this but we don't have that type of capabilities just yet .:)
If you have any more questions feel free to drop us a line at email@example.com. :)