Transaction log growing on a mirrored principal
Mirror, Synchronized / Restoring... is the typical state for the mirror instance.

You can determine why the log file is growing by issuing the following command in a SQL Server Management Studio query window:

SELECT name, LOG_REUSE_WAIT_DESC 
FROM sys.databases 
WHERE name='your_database_here';


This will show several possible choices, such as:

NOTHING
CHECKPOINT
LOG_BACKUP
ACTIVE_BACKUP_OR_RESTORE
ACTIVE_TRANSACTION
DATABASE_MIRRORING
REPLICATION
DATABASE_SNAPSHOT_CREATION
LOG_SCAN
OTHER_TRANSIENT


You may need to perform at least one transaction log backup, among other actions depending on the LOG_REUSE_WAIT_DESCRIPTION shown in the query above.  For instance, there may be a long-running transaction that is forcing the log files to not be re-used.