If my opponent plays Spinning Axe into a 3 might unit, can I Gust it in response?

Yes. Spinning Axe entering the chain opens a Closed State, and since Gust is a [Reaction] you can play it in response — it will resolve first (LIFO) and return the 3 Might unit to its owner's hand. Spinning Axe then resolves, can't attach to the now-gone unit, and enters the battlefield unattached (it'll be killed by its own [Temporary] at your opponent's next Beginning Phase, before scoring).

One caveat: Gust only targets a unit at a battlefield, so this works only if the unit is on a battlefield, not sitting at Base. (RiftJudge FAQ #11482; Chain LIFO, Rule 359.3)