Welcome to Android Central! You can force a shutdown on any Android device by pressing and holding Power for about 15 seconds. The tricky thing is that you might not know when the device has shut down, since the screen is broken. So hedge your bets and hold it down for about 20 seconds or more.
Currently having the same issue. Screen is completely black and I cannot shut off the phone. Tried holding the power button and it did nothing. Tried power and volume down (both connected to charger and not connected) and it only reset it. I'm trying to get the replacement phone working but can't until the old one turns off... and it won't.