You cannot continue your mirror until after your backup has been completed. My software packages allow you to run a POST backup script. If this is the case, you can have your software package initiate the script once complete.
If your software does not do that, you will have to know how long it takes to complete the backup and then schedule the script to be executed.
Whether your create a script, or have your backup software issue the Post backup command, the script is the same. You just issue the command FCPUTIL CONTINUE