No need to remove from the domain (unless you no longer need it at all).
Rename the existing server, give it a new IP address, restart.
Rename new server to the old server's original name, give the new server the IP address that the old server used to be.
That's it.
DNS, assuming you had a static entry for this server, will work as it always has. NAT continues to work as it's just sending traffic to the same IP address.