Managing SQL Server 2008 R2 transaction logs when using principal/mirror databases
Your principal database is in full recovery mode which means you cannot (by rule) shrink your transaction log until you take a transaction log backup.

Here is some information from Microsoft on the subject:

http://technet.microsoft.com/en-us/library/ms191429.aspx

http://technet.microsoft.com/en-us/library/ms179478.aspx

In SSMS, highlight your database in the Object Explorer. Then right click it, choose Tasks then Back up... Next, choose your database. Change your backup type to Transaction Log. Back up to disk somewhere that has plenty of storage (at least as much as your transaction log). 

At 80GB, your transaction log backup will take a long time. Once that's done you will be able to shrink your transaction log. 

I would recommend running a transaction log backup regularly in order to keep your transaction log from growing out of control. 

To answer your question, no, you cannot delete a transaction log (while the database is online) and if you do delete it, you risk losing any data that has not been flushed. 

ALSO, Microsoft says you cannot take a transaction log backup until you run a full backup. If you have never run a full backup on the database in question, run that first before the transaction log backup.