Basic steps for replacing a mirrored disk in software raid using mdadm.

Remove all raid partitions

 
  mdadm --fail /dev/md0 /dev/sdb1
  mdadm --fail /dev/md1 /dev/sdb2
  mdadm --remove /dev/md0 /dev/sdb1
  mdadm --remove /dev/md1 /dev/sdb2
 

Then you can physically remove the bad disk

Once the disk is replaced you need to repartition it. You can use sfdisk to copy the partitions from the good disk.

 
  sfdisk -d /dev/sda > ~/partitions.sda
  sfdisk /dev/sdb < ~/partitions.sda
 

Then you can add the partitions back into the raid to have it rebuilt

 
  mdadm --add /dev/md0 /dev/sdb1
  mdadm --add /dev/md1 /dev/sdb2
 

You can run the following to see the rebuild process

 
  cat /proc/mdstat