One of the biggest weaknesses of a Simulacrum is its susceptibility to Dispel Magic (as the duration says "until dispelled"). So, dispelling a Simulacrum "kills" it in some way.
The Death Ward spell protects against the first effect that would kill the target.
Does the Death Ward spell protect a Simulacrum against the first Dispel Magic that would "kill" it ? I can see a case for both answers, hence why I'm asking here.
Your combo works off the following interaction.
The simulacrum spell description says:
The simulacrum lasts until it drops to 0 hit points.
The description of death ward says:
The first time the target would drop to 0 hit points as a result of taking damage, the target instead drops to 1 hit point, and the spell ends.
Dispel magic deals no damage. It simply removes the simulacrum spell from the target. Sequentially, the simulacrum would revert to snow / ice and melt instantly. Its HP never hit zero as a result of damage.
The same could be argued that you could disenchant a construct and it would stop moving. Any damage to the structure of the construct would remain persistent. If you were able to animate it again - it could be argued the re-animated construct would could have the same number of HP it had before being disenchanted unless time was taken to repair the construct in some way.
Another part of the death ward description says:
If the spell is still in effect when the target is subjected to an effect that would kill it instantaneously without dealing damage, that effect is instead negated against the target, and the spell ends.
The simulacrum is never actually killed. It is dispelled. Again reaching up to my construct example from before - the construct's form still persists without its enchantment, but it isn't outright killed. Neither dispel magic nor ending a spell is a specific death effect. It creates a death-like effect once it's disenchanted.
Additionally, summoned creatures (Summon Monster and its variants) that are dispelled aren't killed either, they are dispelled. And do not trigger necromancy like effects such as Dark One's Blessing (warlock) or Grim Harvest (Wizard).
Relevant Topic: What happens when you target dispel magic at a summoned creature?
The wording of the Dispel Magic spell is:
Choose one creature, object, or magical effect within range. Any spell of 3rd level or lower on the target ends. For each spell of 4th level or higher on the target, make an ability check using your spellcasting ability. The DC equals 10 + the spell's level. On a successful check, the spell ends.
At Higher Levels. When you cast this spell using a spell slot of 4th level or higher, you automatically end the effects of a spell on the target if the spell's level is equal to or less than the level of the spell slot you used.
Emphasis on "any spell". One casting of Dispel Magic can dispel all spells applied to the target.
There is nothing in Death Ward that negates being dispelled. So assuming Dispel Magic is cast at the 4th level or otherwise passes the spell DC, Death Ward would drop. Likewise if cast at the 7th level or passing the spell DC, Simulacrum would also drop.
There is one possible exception however. Suppose that Dispel magic is cast at 3rd level, the roll for Death Ward fails, and the roll for Simulacrum succeeds. Thus, Death Ward is still up, but Simulacrum would drop.
Considering a Simulacrum is defined as a creature that has hit points, and dispelling would effectively kill it without dealing damage, your interpretation appears to be correct. In this one circumstance, the most logical ruling seems to be that it should be saved.
