Will the ''wipe data/factory reset'' in ClockworkMod also remove my backups I have done? I currently have CyanogenMod 10.1 (Android 4.2.1) on my Galaxy SIII. I used ClockworkMod to flash the ROM.

Now, after using the ROM for a while, I want to try some other ROMs, so I made a backup of my current ROM (CyanogenMod 10.1) in ClockworkMod recovery and the backup was saved to: /mnt/shell/emulated/clockworkmod/backup.

Now, if I use the "wipe data/factory reset" option in ClockworkMod recovery, will that remove the backup I made?
Wipe data will wipe everything on your /data partition (hence the name). A factory reset will wipe the same (additionally also cache and Dalvik cache), and put your device back to a virgin state. Usually, this doesn't touch the (external) SDCard, and AFAIK should not touch the internal SDCard either.

I don't know on which partition your mentioned folder resides; but if you want to be on the safe side, back up everything to the external SDCard (or even better off-device, e.g. to your computer).