Yes, of course, it's possible. But, it's not easy, unless you are experienced with all the tools and have done it a few times.
Can you shut down the services? That would be the easiest solution. Stick another drive in, clone the partition maps in single user mode, dd the partitions from one to the other. Move it to a different machine. Reconfigure reboot.
If you can't do that, then life gets more interesting. You're still going to need some downtime or transition time. You could install everything for a new machine, transfer the data over, then redirect the service definitions (DNS) to point to the new machine. Getting the data over requires dumping MySQL, transferring, importing. But then when you make the transition, you will still have transactions that you will have to transfer over to bring the new one up to date with anything that happened on the old one before you shut it down. Unless you have the freedom to simply shut it down, transfer the data, and then bring it back up.
For starters, you can look at this:
http://www.mysql.org/doc/refman/5.1/...mysqldump.html. But you are probably going to have to do a fair bit more reading to get comfortable with the task at hand.
As you zero in on what you really need, ask more questioins.
