How to stop the death waves in my city?

The cause of the problem is that when you zone a whole residential district all at once, many adults move in at roughly the same time, then they become seniors (and eventually die), at the same time.

There are a few solutions available to you:

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1. Build Slower

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The first solution involves preventing the population spikes that result in the mass die-offs. Build out your residential areas slowly - You can pre-build all the necessary roads and infrastructure - but only zone a block at a time, leaving a half-year to year long gap before adding the next block of residential. This will space out your population and result in more staggered deaths.

While this can work, if you are working with a particularly large residential area, it can get tedious. You can probably get away with zoning more light residential at the same time, as fewer citizens can move into each building.

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2. Deal with it

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This can be more difficult as it relies on having fairly un-congested roads. The problem with crematoriums is that even if they have sufficient capacity to deal with all the deaths, they have a limited number of hearses to collect the bodies. The solution is to build a bunch of cemeteries near the edge of your map, and have them inactive until they are needed for a death wave. After the bodies are collected, you can empty the cemeteries into the crematoriums (Be sure to empty all the cemeteries at the same time, or they may just empty into an open cemetery).

You will still have the population swings for a while until things stabilize. But it will at least prevent high level buildings from being demolished due to not collecting the bodies fast enough.

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3. Managing the RCI demand

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As residential demand goes down, industrial goes up. Industrial down = residential up. But the solution to death waves is a little less obvious: When residential demand is up - build industrial. when industrial demand is up, build residential. This helps mitigate bubbles that develop in the cycles. This guide by Badben on Steam explains it best:

1, Whenever you build new residential zones, only adults move in. The first time you build residential, you are creating your first population bubble, a large percentage of your population that is the same age.

2, Those adults have children at the same time, which becomes your second population bubble.

3, the population bubbles age. When the first bubble of adults become seniors, their children become young adults, when those seniors start dying, their children become adults and start having children, growing a new bubble.

4, When adults start having children, your population starts rising, and they demand more housing.

5, you build more residential zones, which attract new adults from outside of the city. This is like throwing oil on a fire. You are adding new adults on top of a bubble of adults, making the situation worse.

If you zone residential when the demand bar is at it's lowest, means, you're adding new adults into the city in between two other bubbles. One bubble will be seniors, and the other young adults. By adding more adults at this time, you create new population bubbles to offset the ones already there.

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4. Mod it.

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Citizen Lifecycle Rebalance

Among the other things this mod does is alter the ages of citizens that migrate into your city. Instead of them all being the same age when they move in, they will now be a wide variety of ages. This will reduce the chance of seeding your city for mass death waves.

Be aware that using mods will disable achievements, if those are things that are important to you.