I am going to assume you mean maintaining a pair of servers and mirroring the data between them.
This is a very complex question, the answer to your general question is yes, you can do this but there are many aspects to consider like performance, rate of change, snapshots etc.
Mirroring (replication) does NOT replace backups. You could argue that replication + snapshots could replace backups but that's debatable (I think when done well it is but others would disagree).
You should look at the rsync utility. At a minimum it's capabilities will give you an idea of what is possible and how to set it up. There is also "synchronous replication" where each write is done to both locations before being acknowledged as successful. This is quite a bit tricker to do properly and can require a large low latency network connection if you have a high rate of change for the data you are replicating.