Can Mordekaiser, Twice Slain save himself by killing another friendly unit that is about to die with him?
Yes, if Mordekaiser's once-per-turn replacement effect is still available.371.1 This includes another friendly unit that is about to die from the same combat.
Combat damage itself does not kill either unit. The kill action happens during the combat cleanup that follows, which would kill all units with lethal damage simultaneously.467.2.d468.1323.4370.1.a.2 Here, "simultaneously" describes the kills that cleanup is about to perform; it does not mean those units are already dead.
Replacement effects apply before the events they replace, so his effect steps in before the cleanup kills happen.370.1.c At that point, the other friendly unit is still on the board. It may have lethal damage and be about to die, but you can still kill it to pay the cost of saving him.740.4.a Paying that cost performs a separate kill action before cleanup performs any simultaneous kills left unchanged.203.1373.1.a His own death is replaced, so he is healed, exhausted, and recalled instead.
The same timing applies to spells outside combat:
- Damage followed by a cleanup: If Singularity or Bellows Breath leaves him and another friendly unit with lethal damage, the cleanup waits until the spell finishes resolving.321321.1 That cleanup would then kill them simultaneously.323.4370.1.a.2
- One kill instruction: The Ruination and Cataclysmic Duel each have one kill instruction that can kill multiple units, so any deaths caused by that instruction are simultaneous.370.1.a.2