Can you activate a mana ability in response to a spell being cast before it resolves?

Mana abilities are special: they do not use the stack and cannot be responded to (CR 605.3b). This means you can activate a mana ability essentially at any point you have priority, including after a spell has been cast and is waiting on the stack to resolve.

However, there is an important nuance. Mana abilities are most commonly used during the process of casting a spell — specifically in the payment step — to generate mana to pay that spell's costs (CR 601.2h). If you want to use the mana to pay for a spell you are currently casting, you activate the mana ability as part of that casting process, not 'in response.'

If a spell is already on the stack and you want to activate a mana ability before it resolves, you can do so when you have priority. For example, if your opponent casts a spell and passes priority to you, you may activate a mana ability to float mana in your mana pool before you cast your own instant or before the spell resolves. The mana ability resolves immediately without going on the stack (CR 605.3b).

Concrete example: Your opponent casts Lightning Bolt targeting you. You now have priority. You tap a Forest for one green mana (a mana ability), then cast Giant Growth on your creature. Lightning Bolt is still on the stack, and you generated the mana mid-stack without any issue.

Keep in mind: mana empties from your pool as steps and phases end (CR 500.4), so floating mana for too long is usually not productive unless you spend it right away.