Yes, but you don't provide enough information to understand what you are asking exactly.
Generally changing a domain between two servers is pretty simple:
1) Set up new site and email and test.
2) Set up your email software to check at new server using IP address while keeping old email account information. (You need to check 2 places during the switch)
3) Change DNS to point to new site. (You may also choose to set up a re-direction from the old site to the new one so that during this transition time all traffic lands on the new site.)
4) After 5 minutes to 24 hours when you are sure all traffic and email is going to the new site, check your mail at the old server one last time, then remove the old site. Remove the old email account in your computer.
If you have a database on your site it can be a little more complicated...
If you know what you are doing with the DNS, you can change the "Time to live" setting so that the time needed up update all DNS servers is much less than the normal time.