Can I mark damage first and then reduce a unit's might to kill it?

Yes, you can. A unit will be killed if it has non-zero damage marked on it that is equal to or exceeds its current might.

According to the RiftJudge FAQ #3880 and FAQ #2662, the order in which these events occur—whether you deal damage first and then reduce might, or reduce might and then deal damage—does not matter. The game state is checked, and if at any point the damage marked on a unit is equal to or greater than its current might, that unit dies.

Example Sequence:

1. A unit has 3 Might and 0 damage marked.
2. You deal 2 damage to the unit. (It now has 3 Might and 2 damage marked; it survives).
3. You play an effect that reduces the unit’s Might by 1.
4. The unit now has 2 Might and 2 damage marked.
5. Because the marked damage (2) is equal to its current Might (2), the unit dies.