how back up iphone with dead screen

You cannot do so if you cannot unlock the display. That is a requirement to be able to execute either an iTunes or an iCloud backup.

Hopefully you’ve been using automatic iCloud backups or have been making fairly frequent iTunes or finder backups. Otherwise, you’re going to lose data.

To learn "How to back up your iPhone, iPad, and iPod touch" click here --> https://support.apple.com/HT203977

You will see that one of the things you are required to do is enter your passcode which you cannot do on a device with a display that is not working.

If you've never backed up the phone, it's too late to do so now.

~Lyssa

If the device is still working but it is simply the display that is bad, then if you are lucky and had it set to backup to iCloud automatically then you're in a good position.