Does your touchscreen still accept input? If it does, you can try locking your screen, pressing the power button (a non-brocken screen would turn on) and hold down both volume buttons to enable Talkback.

Talkback will read aloud what is visible on the screen. If you never configured it, it might be hard to understand depending on your language settings and the talking speed.

But with some patience you should be able to navigate to where you need to and enable the USB datatransfer to backup your data or navigate to the settings menu to enable ADB debugging for a full adb backup.