"has there been a case in which speaking one's mind has caused their death"The case that immediately sprang to mind for me was that of Alan Berg[1], a radio host who was assassinated (and about whom Oliver Stone made a movie called Talk Radio[2]).
But this has happened many times throughout history, where people were assassinated (or imprisoned/executed) for their beliefs.
More modern instances are things like journalists being assassinated in South America, for instance, for reporting on organized crime (similar things happening in Italy), or in Russia for criticizing Putin, or in the Islamic World for incurring the wrath of religious fanatics.. or the Charlie Hedbo attacks in Paris, or various beheadings of journalist and teachers.
Some older, but still relatively recent and famous cases have been the assassinations of Martin Luther King Jr, Malcolm X, and Gandhi... etc.
Of course, speaking one's mind against the rulers or their system in a totalitarian state like Nazi Germany or the Soviet Union has always been a quick path to the gallows or a concentration/labor/death camp.
[1] - https://en.wikipedia.org/wiki/Alan_Berg
[2] - https://en.wikipedia.org/wiki/Talk_Radio_(film)