I would start this test FIRST by taking a copy_only backup, see here for details, of DB1 on server 1.
BACKUP DATABASE [DB1] TO DISK = N'<backup location>' WITH COPY_ONLY
This will let you get back to ground zero at the end or if something get messed up. Then you can turn off mirroring using the command
ALTER DATABASE DB1 SET PARTNER OFF;
After mirroring is turned off I would backup the tail of the log, see here for details, using the command
BACKUP LOG DB1 TO DISK = N'<backup location>' WITH NORECOVERY;
and then restore that backup to DB1 with recovery. That will bring the DR site online. At that point you can then setup mirroring from server 3 to server 4.
*Note: Script this out as much as possible. You do not want to be trying to do this manually if this was a real DR situation.
Also, if you have log shipping on server 1 and it is mirroring to server 2 you should setup all the log shipping jobs on server 2 so if you have a failover you can quickly enable the jobs and start log shipping from server 2 to server 3.
At the end of your testing you can restore the copy_only backup to server 1 reset up mirroring to server 2 and log shipping to server 3.
Hope that helps.