@OP, I think you should make it clear that the groupon link you have is a referral for your account.
The information provided by the OP doesn't seem to be valid as well. There is no partial redemption and you cannot combine the groupon offer with the AMEX free tie offer. Both the AMEX and the groupon code are applied as promotional codes, and you can only apply one for each order. The groupon code can only be applied through the link ctshirts.com/grouponus, whereas the AMEX code can only be applied through the link provided in the OP.
Damn, you're right. Out of curiosity even though my Groupon isn't usable until tomorrow, I tried it and it's treating it as two different things since it will only take one code as you said.