Death offering and Mirage = Death?

There's no info about that interaction, we will die if affected by offering when we enter in mirage map?

That might depend on the situation, depending on what takes priority and how the interaction with players not being able to die actually works. If you are in a Mirage area with the effect that players cannot die, then it is possible that Death Offering would not kill you.

At the same time, I do have to question why you are asking such a very specific scenario. If you build around it, you would either prevent yourself from being affected by Offerings and therefore never die from it, scale the duration high enough that it would not kill you in the first place, or run a trigger setup to ensure the Offering effect is active at all times. There is realistically no situation where you would deliberately rely on the single moment of interacting with a Mirage zone and its inability to kill players just to make use of that interaction.