Are the disks the same size? If so, I suspect you could just use dd from your LiveCD environment:
dd if=/dev/sda of=/dev/sdb
Just, be really careful that you know which disk is the old one and which is the new one, because disk destroyer will blindly copy, bit for bit, with no regards for what it's actually doing. What's neat though, if you do this, dd will copy over your MBR as well (it will copy the *entire* disk), so it might be a single command, then take the old drive out, and reboot.
If the new disk is larger you can still do something similar like this, but you might have to then resize partitions to make use of the new space. I haven't played with that in a while, so I don't know the exact commands, but it should be pretty easy to google. They're likely file system dependent in any case.