Geas does not work in a DMZ
The 'rules' for Dead Magic Zones (DMZ) can be found in the Weird Locales1 table on page 109 of the Dungeon Master's Guide:2
Dead magic zone (similar to an antimagic field)
So looking at antimagic field:
Spells. Any active spell or other magical effect on a creature or an object in the sphere is suppressed while the creature or object is in it.
And as geas is a continuous spell (i.e. has a duration) it is suppressed while the creature is in the DMZ. Being suppressed is explained as
While an effect is suppressed, it doesn't function, but the time it spends suppressed counts against its duration.
so it should not force the command, nor deal any damage for failure to comply.
1: A set of some fantastical things a DM can put in the Wilderness of their world to make it more, or in this specific case less, magical.
2: If your DM is using different rules for DMZs I can't help you.