I would like to setup Mercury so when a User logs in they can only send and receive emails from other Users on the same server. There would be no way to send to or receive from any other IP address.

Could someone please explain to me how I would accomplish this using Mercury?

MercuryS (the SMTP server module) can be instructed to never deliver mail to non-local addresses by selecting strict local relaying restrictions in the Connection control tab in settings. See Mercury help for more details.

To prevent non-local senders from submitting any messages you could enable transaction level filtering in the Compliance tab, and create a rule similar to this one:
M, "@mydomain.com", R-N, "554 Sender address not permitted"

That should cause messages from anyone with a MAIL FROM: address other than those belonging to your domain to be rejected.