Yes, of course the log can grow because of mirroring.
Please read through this: http://www.sqlservercentral.com/articles/Transaction+Log/72488/
I'm not a mirroring expert, check the transmission and redo queues and maybe post another thread specifically for mirroring problems.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability