Amazingly, if you are using Windows Server Backup, you have no way to delete old backup files. The service is supposed to simply grow your backup data until your drive is full, and then it should start cleaning up the old backups, but that isn’t ideal.
I found that I was able to delete the oldest backup by using the command:
delete shadows oldest f:
Where f: is the drive that is used for backups. There is no way to tell it to keepLatest 100 like you can if you were just deleting the system state, but you can put a bunch of delete commands into a text file and point diskshadow at it.