If I have two units in my base and my opponent uses Cull of the Weak, can I use Deathgrip on the unit that I chose? Will I still have to pick the other unit for Cull of the Weak?

To answer your question, we must look at the timing of how these spells interact on the chain.

The Ruling

Yes, you can use Deathgrip in response to Cull the Weak.

If you use Deathgrip to kill one of your units, that unit is removed from the board before Cull the Weak resolves. When Cull the Weak eventually resolves, you will still have to make a choice for its effect, but you will have to choose from the units you have remaining at that time. If you have no other units left, you simply do not kill one (as per the "do as much as you can" rule).

Sequence of Events

1. Opponent plays Cull the Weak: They place it on the chain. It does not target, so no choices are made yet.
2. You play Deathgrip (as a [Reaction]): You place it on the chain in response to Cull the Weak.
   • As part of playing Deathgrip, you must target and choose a friendly unit to kill (FAQ #9315).
3. Chain Resolves (LIFO - Last In, First Out):
   • Deathgrip resolves first: You kill your chosen unit. Because you killed it, you trigger the rest of the Deathgrip effect (giving Might to another unit and drawing a card).
   • Cull the Weak resolves second: Now it is time for you to fulfill the instruction "Each player kills one of their units."
4. Final Choice: You must now choose a unit to kill for Cull the Weak.
   • If you have another unit remaining, you must choose one to kill.
   • If you have no units remaining (because you only had two and Deathgrip killed one, and you have no others), you perform as much of the effect as possible—which in this case means you do not kill any unit, while your opponent must still kill one of theirs (FAQ #204, #8657).

Note: This interpretation is based on the rules for targeting and chain resolution. No official FAQ exists for this specific interaction between these two cards, but it follows the established mechanics for how [Reaction] spells and non-targeting spells interact.