I have done a SQL database mirroring setup. There is a Sql job which takes continues full database backup daily. Should I stop this job ?
No, you still need to take backups including FULLs and LOGs (DIFFs work too, just depends on your set up).
Make sure you are taking LOG backups as well, or your log file will get full and things go breaky.
All mirroring does, depending on what mode (async or sync), is keep data in sync between your primary and secondary.
Synchronous means the transaction needs to happen on both primary and secondary servers before it's considered complete.
Asynchronous doesn't require the transaction to complete on both sides (think of a server in NY and one in CA, latency would make things very slow if you have to commit a transaction on both sides of the country).
You still need to take backups as you normally would. What if both servers go down and you lose them? Those backups are the only way to get your data back.
Ideally the mirror db instance acts as the backup for the principal. So you already have a hot standby for the data in your principal in the form of the mirror dbs
You cannot take backups of the Mirror databases as they are in restoring mode..obvious..ain't it?
As of Principal, you can take continue to take your full backups.