Making a NANDROID backup of a device with broken touchscreen
The "classic CWM" does not even support the touch screen. It is operated solely via hardware keys -- usually the volume up/down keys to navigate, and the power button to confirm actions. On devices featuring a trackball (as the "classic htc-wildfire for example), this can be used as well to scroll the menus and confirm actions.

Note that there's also a touch-enabled CWM available -- but that's not the "classical one".

However, if your device comes from the manufacturer, it is not equipped with clockworkmod, but with a stock recovery. Stock recovery does not support nandroid backups. So you would first need to flash the recovery in order to use that. Depending on the device, there may be different installation instructions (and different requirements), so make sure to check that first. CWM would then replace the existing "3e" recovery located on the /recovery partition, but should leave the other parts (e.g. your /data and /system) intact.