Force quit Time Machine, then shut down the computer (if the entire computer is unresponsive then holding down the power button for about 10 seconds will shut it down by force, better to shut it down normally if you can). Then restart, see if it works as expected. If not, shut down again. Then restart in Safe Mode (holding shift key down, which can take some ~ minutes). When it finally boots in Safe Mode it should say Safe Boot in small red letters somewhere on your screen. Then restart normal and retest.
If the problem persists, connect the Time Machine disks one at a time and run Disk Utility to do First Aid on each external Time Machine drive in turn. That is to check that some problem with the external drive is not freezing your Mac. A failing connected external drive can cause a Mac to be unresponsive.