I don't believe there has ever been a death of a character due to a tank-related incident. However, this is largely due to safety precautions taken by the officials in charge of the tank activities. (And also, a bit of anime physics.)
From the (fan-)translated Rules of Panzerkraft:
3-02 Supplemental Equipment
Furthermore, for the safety of the participants, the crew compartments are required to be fitted with League-approved armored mantles as an added safety measure.
3-03 Usable Cannons
All rounds are to be League-sanctioned live ammunition; production of your own warheads or charges is not allowed.
5 Prohibited Actions
a) Using unregulated equipment or parts
c) Firing directly on humans
Note the usage of controlled armor, rounds, and a rule that you may not fire at a human. So, it does appear that the tank warfare is dangerous to people, but the safety measures in place are enough that the direct warfare does not cause any fatalities or serious injuries. (I think there's an incident where one girl has her glasses broken, but that's it.)