In the usual RPG game, the death of a deity is trivial. In fact, killing a deity is a trivial task if the deity is given stats, as long as of course the PCs are high level enough, but that's all it takes. As such, the consequences are also trivial... you may get some earthquake here and meteor swarm there, even major cataclysms but guess what, the PCs are going to survive whatever so even if destroys a continent it will still be trivial from the PC's point of view. That's what happens in most games featuring the death of a deity, but that' because after all a killable deity is not much more than just a very high level creature.
Now, if you really treated deities in a RPG as deities are narrated by real world religions, things would be wildly different. Killing the "God of War" wouldn't be a matter of stabbing it enough times until it's down to 0 hp. Perhaps it would require to somehow end all wars in the world, and erase the concept of war from the minds of the people so that there won't be more wars in the future. That's if you treat the "God of War" as the embodiment of the concept of war itself. Presumably the opposite could be true i.e. if you managed to physically kill the God of War you might have the effect that all wars stop because the concept of war disappears from the people's mind. Either way, this approach pretty much means that practically deities don't die. But that's probably not fun for a lot of players, and this approach is followed only by DMs like me who just don't want to deal with that kind of narrative with PCs wanting to ascending to godhood themselves and change the pantheons.
It is possible to have a sort of doable compromise between the two extremes. For example, deities may not be as much as the concepts themselves, but effectively mere proxies for those concepts. This is basically what Forgotten Realms does with the idea that each deity is simply an extremely powerful being which oversees a portfolio of concepts: when a deity is removed, the portfolio becomes vacant but is quickly claimed by competitor deities. This idea can definitely spark some interesting effects on the game while still making it manageable: perhaps the death of the current "God of War" would affect all existing wars in the world leading them to a stall... strategies fail for no apparent reason, any sort of impediment come up unexpectedly so that it becomes difficult to start new wars or win existing ones, newly crafted weapons come up defective and existing one rust more quickly. Generally speaking, I would focus on stuff strongly related to the portfolio, not just general catastrophies, and try to use it to twist the campaign significantly for a few character levels at least.