How To use your android phone with a completely broken screen.

Use your android phone to backup data when your screen is unusable or non responsive due to external Damage 

Worried..?

For this you would need:

• A broken android phone ( non broken would would produce the same result :P )
• An OTG [on the go] USB cable.

You could get yourself a pair of otg cables online from Amazon.in you could get it below 100bucks

 Usb OTG

• An optical mouse with a USB port.

well you could use the same one from your computer or get one from Amazon.in

Usb Mouse

If you have all of the above, simply just connect the the OTG to your Android™ device. Similarly to your charger pin and the mouse on the other end of the OTG device. Now, when you do it, your device will be totally accessible. It is highly advised that you back up all the things you need before sending it for a screen repair.

This could be also done for adding additional storage to phones that come only with internal memory, usb keyboards and some game pads are also compatible try your luck with your device.
the basic criteria is that your device should be capable of usb host.