Can you regenerate a creature in response to it being exiled by a spell?

Regeneration creates a replacement effect that replaces the event of a creature being destroyed. It does not protect against exile, sacrifice, or any other way a creature can leave the battlefield. This is clearly established in CR 701.15a, which defines regeneration as replacing destruction specifically, and CR 700.4, which confirms 'destroy' and 'exile' are distinct game actions.

Even if you activate a regeneration ability in response to a spell that exiles a creature (such as Path to Exile or Swords to Plowshares), the regeneration shield will be set up but will never trigger. When the exile spell resolves, it moves the creature to the exile zone — it does not destroy the creature — so the regeneration replacement effect has no applicable event to replace and simply does nothing.

Regeneration also requires the creature to survive until the replacement effect is relevant (CR 701.15b). Since exile happens immediately upon spell resolution and is not 'destruction,' the shield is wasted entirely.

Example: Your 2/2 Grizzly Bears is targeted by Swords to Plowshares. You activate Darkpact Shaman's regeneration ability in response. Swords to Plowshares resolves, exiling Grizzly Bears. The regeneration shield does nothing — the Bears go to exile, not the graveyard, and are not considered destroyed.

If you want to save a creature from exile, you need a different type of protection — such as giving it hexproof (so the spell can't target it), or blinking it with a spell like Cloudshift that moves it out of the way before the exile resolves.