Since the op is asking for killing the display server you can look for Xorg server pid with
ps -H -t /dev/tty1
and then kill it with
kill -SIGKILL <pid-obtained>
to restart the server
startx
this would bring up the sddm login screen. However this isn't what you probably need as simply restarting the plasmashell or kwin should do the job.
You should start testing with the less destructive plasmashell replace. you can set this command as a keyboard shortcut since you mentioned your keyboard works during the issue and work your way to the kwin
for plasmashell:
killall plasmashell; kstart5 plasmashell
and for kwin
setsid kwin_x11 --replace &
PS: sorry I accidentally replied to filo and now I can't change it. 