What is it that you're backing up? A relational database? Misc files?
How much downtime can you afford? (if you want low downtime then you really must start planing for unscheduled outages - meaning you need at least one other machine).
If it were me and there was a need to minimise downtime I'd break a disk out of the mirror (if there's a DBMS running on it then stop it first, break the mirror and restart to get a consistent snapshot). At most you're looknig at a few seconds of downtime. Then remount the filesystem from this disk somewhere else for backup. It can then be hot-joined back into the raid set.
There are ways to maintain the service when creating a consistent snapshot - but these are specific to the DBMS being used.
As for getting the data off the hard disk....for a DBMS, use the DBMS tools for generating a backup - a file image may not be portable across different versions of the DBMS. Every DBMS I've come across will allow you to run 2 instances on the same machine (as long as they are using different data files / network sockets).
Don't use dd or dump - in addition to no error checking, there can be portability issues with these too. cpio and tar have been around for a long time, tar can tricky when bitflips / corruption occurs. I've been using afio for some time - it allows individual files to be compressed (rather than tar compression where the output stream is compressed).