I cast Stupefy on a unit, then opponent responds with Thrill of the Hunt on it. He plays then the unit on another Battlefield. Does my Stupefy still resolve after this and the unit take the minus one might?

To answer your question: No, your Stupefy will not reduce the unit's Might.

While your Stupefy will still resolve and allow you to draw a card, it will fail to apply the -1 Might effect to the unit. Here is the sequence of events based on the Riftbound rules:

Sequence of Events:

1. Play: You play Stupefy targeting a unit on the battlefield. It is placed on the chain.
2. Reaction: Your opponent plays Thrill of the Hunt in response. It is placed on the chain on top of your Stupefy.
3. Resolution - Thrill of the Hunt: Thrill of the Hunt resolves first. It banishes the target unit, and then its owner plays it to a new battlefield.
4. Object Change: According to Rule 705 and as confirmed by RiftJudge FAQ #9870, when a unit is banished and then re-played, it enters the board as a "new object." It is no longer the same game object that your Stupefy targeted when it was played.
5. Resolution - Stupefy: Now it is time for your Stupefy to resolve.
   • The original unit is gone/changed. The new unit at the other battlefield is not considered the same object, so it is an illegal target.
   • Per Rule 359.3.e.5, because the target is now illegal, the instruction to "Give a unit -1 might" is ignored.
   • The second part of the card, "Draw 1," does not require a target and is not dependent on the first instruction. You will still draw your card.

Summary

Because the unit became a "new object" when it was re-played by Thrill of the Hunt, your Stupefy effectively "mistargets" the original unit. Your spell resolves as much as it can (drawing the card), but the Might reduction fails.