From how I understand what you are asking, the short answer is: Sorry, you can`t do that.
If you are at any point handling any data from a client (i.e. an email), then there is simply no way you can prove conclusively to that client that you are not at any point keeping a copy of that data. If you did want to keep the customers data, there would simply be to many ways for you to do it discretely for it to be practically possible for a customer to catch you doing it.
In the end, it will therefore come down to a question of trust; you basically have to convince your customers that you do in fact not have any intention of keeping their data, and hope they believe you.
Side note / alternative:
If all you are doing is forwarding mail which is sent to a specific domain, then perhaps providing your customers with a guide to using encryption might help? Then you can tell your customers:
Do this, and you're data will be securely encrypted, no matter where you send it. Now we have no way of knowing the contents of your data. We'll just forward it safely to your personal account for you.
The main catch I can see regarding this is that you could in theory still retain a substantial amount of meta data about your clients. This might for instance include statistics about how many emails have been sent, from and to where/whom they were sent, possibly including server names and IP addresses that may give hints about locations, affiliates, etc.
If this is important, then you're basically back to the question of whether your customers trust you when you presumably claim that you will never keep any such data.