If the opponent plays Cull of the Weak, can I react to the unit I chose to die with Thrill of the Hunt to banish it and save it by replaying?

To address your question: Yes, you can use Thrill of the Hunt to "save" a unit from Cull the Weak, but your unit will still likely die.

While Thrill of the Hunt removes the specific unit you targeted from the board and plays it back to a battlefield, the effect of Cull the Weak is not tied to the unit you initially "chose" when the spell was played (as Cull the Weak does not target).

The 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 Thrill of the Hunt (as a [Reaction]): You place it on the chain in response to Cull the Weak. You choose one of your units to banish and then play to a battlefield.
3. Chain Resolves (LIFO - Last In, First Out):
   • Thrill of the Hunt resolves first: The unit you chose is banished and immediately played to a battlefield. It is now a new game object at that location.
   • Cull the Weak resolves second: Now you must fulfill the instruction: "Each player kills one of their units."
4. Final Choice: Because Cull the Weak does not target, you are not locked into killing the unit you originally intended to protect. However, you must choose a unit you currently control to kill.

Why the unit will likely still die

If the unit you re-played using Thrill of the Hunt is the only unit you have on the board when Cull the Weak resolves, you are required to choose that unit to be killed.

• Rule 359.3.e.11 ("Do as much as you can"): This rule only applies if you have no valid units available to kill. If you have even one unit remaining on the board (even the one you just re-played), it is a valid unit and must be chosen.
• Targeting vs. Instructions: Because Cull the Weak doesn't target, you don't "choose" the unit until the resolution step. Any unit you control at that moment—including the one you just re-played—is a valid choice to fulfill the kill requirement.

In summary: Using Thrill of the Hunt in response allows you to change the location of your unit or trigger "When played" abilities, but it does not bypass the requirement to kill a unit for Cull the Weak. If that unit remains your only unit, you will simply have to choose that same unit to fulfill the requirement when the spell resolves.