How to enable debug mode on Sony Xperia V with broken touch screen?
There are several options available for you.


Given you have enabled USB debugging, you can use Droid@Screen to view the android screen on your PC and control it. (So you can get backups through the PC)
You can use an otg adaptor to control your device using a USB mouse. (So that you can use whatever the app you want to back up your device)