You don't need superSU with Cyanogenmod 13, it should already have super user implemented with the ROM already. You probably used the wrong version of SuperSU or something. Usually the latest SuperSu binary is more reliable for marshmallow / Android 6.0+. Sounds like either rom or superSU needs to be reflashed (I don't think wipe data / factory reset via recovery is necessary.)
Always do Nandroid backups in recovery. This means using the backup function in CWM or TWRP to backup your whole rom so that you can easily restore it in recovery if it bricks agian.
I'm guessing booting recovery or download mode is the same on a nexus phone?
When phone is off:
Download mode: Volume Down + Power?
Recovery Mode: Volumpe Up + Power?