Only (A) is correct.
a) The doctor said two kids choked to death due to inhalation of mud.
b) The doctor said two kids were choked to death due to inhalation of mud.
Forget the rest of the sentence, just consider the part with/without the auxiliary:
Two kids choked
Two kids were choked
"Two kids choked" means that they involuntarily choked - perhaps on food, or something else that blocked their windpipe.
"Two kids were choked" means something or maybe somebody choked them. If you include this auxiliary verb you need to say what, or who choked them, using "by" for example:
Two kids were choked by food.
Only when you omit the auxilary verb can you use "on" and say:
Two kids choked on their food.
Your example uses "due to", so it is citing a cause, not necessarily the item that they choked on. Consider this example:
Two children were choked by food due to not chewing it properly.
In this example, the direct cause of the choking was still the food, but the underlying cause was that the food was unchewed. Only sentence (a) makes sense because it links the cause to the effect.