See http://gregmaxey.mvps.org/Extract_Form_Data.htm

There is no out-of-the-box feature in Word designed to deal with this, but I
wonder what facilities already exist to extract data from these incoming
messages? EIther someone designed and implemented a complete system that
creates the forms, puts them on the web server, collects them in a public
folder and then does something with them, or you happen to have the first
part of that system but not the last. (NB, there are facilities in Access
and Outlook 2007 designed to do data collection via e-mail - I have no idea
what they are like or whether you are in a position to use them, but it may
be worth looking).

If there are no such facilities, you would need to know more about the
format of these e-mails and write some code (e.g. perhaps using Word VBA and
the Outlook object model) that can extract the data and stuff it directly
into a Word document. And no, I don't get to see my Public Folders in the
Export dialog box in Outlook either.