Shouldn’t it be “…the dead of injured”? Is “the” missed here?

"The dead of injured" makes no sense. Dead people aren't injured and injured people aren't dead. To be injured, you must necessarily be alive. "And" is necessary because it's not the count of dead or the count of injured. It's the summation of both.

Technically it can work either way. "Dead" and "injured" are used as shortened versions of "the dead" and "the injured", where "the" is implied but not stated. It's common in writing when the author wants to emphasize the state of the people (being dead or injured) rather than the individuals themselves.

I'd say it's easier to think about it as "*...the toll of dead (people) and injured (people) mounted*. "The dead" and "the injured" are basically just formal ways of saying "dead people" and "injured people" anyway. The point of the sentence is to say that the human "cost" kept increasing, in terms of both death and injury.

Ask yourself who is likely to know best - you or a dictionary?

It’s sort of a weird example. Firstly, You’re using it to replace a group of countable nouns (plural) into a singular. In this example It’s the same rules if you were using “number”: “the number of dead and injured mounted” It wouldn’t makes sense to add a definite article before the adjectives “dead and injured”. They are modifying the word “toll”, so adding “the” is superfluous. You can’t make “toll” double definite. There are other situations where you COULD use “the” after “of” though. It would just need to be in reference to a second noun. “The toll of the earthquake was severe” Though I suppose this is a slightly different sense…

some weird rule about using 'the' twice in a sentence. it sounds odd and could be either way. please Google that for us first