You would implement a "smart host" for your MTA. This tells the MTA to hand off the outbound emails to another server for delivery... so:
Server A - No external internet connection, needs to send emails. Networked internally.
Server B - External internet connection with an MTA to send the emails out.
Email is generated on server A, hands off the email to Server B "Smart Host", which then sends the email out.
Do some google searching for "postfix smart host setup", heres a quick synapses of config files and how they can be setup for this to work: http://www.bergek.com/2009/02/22/con...se-smart-host/