if the opponent has vex apathetic at a battlefield with 1 damage. and i play watcher. will it die to the -3 before it stuns my watcher? or does watcher get stunned and Vex dies?

Yes — both happen: Vex's trigger still resolves and Stuns your Watcher, and Vex dies afterward to the -3 with 1 damage on it.

Walk through it: Vex, Apathetic is 4 Might, so Thousand-Tailed Watcher's "When you play me" trigger drops it to 1 Might (the "minimum of 1" clause is the floor). Because you're the turn player, your Watcher trigger goes on the chain first and Vex's trigger goes on top, so it resolves first and Stuns your Watcher plus stops you moving it this turn (Rule 383.3.d.1). Your trigger then resolves, Vex sits at 1 Might with 1 damage marked, and it's killed in the following cleanup — a reduced-Might unit dies to damage already on it.

Even if the ordering were reversed, the result is the same: once Vex's trigger is on the chain it resolves independently of Vex's death, and the Stun and "can't move it this turn" effects persist for the rest of the turn (FAQ 12412). So your Watcher is Stunned, but it stays on the board at 7 Might since the -3 only hits enemy units.