Can you activate mana abilities in response to other mana abilities?

Mana abilities are a special category of abilities that resolve immediately without using the stack (CR 605.3b). Because they never go on the stack, there is no window between their activation and their resolution during which another player could respond. This means you simply cannot respond to a mana ability the way you would respond to a spell or a triggered ability.

A mana ability is generally defined as an activated or triggered ability that could produce mana and doesn't target (CR 605.1a, 605.1b). Examples include tapping a Forest for green mana or using Llanowar Elves. When you activate such an ability, the mana is produced instantly — no one gets priority in between.

You can activate your own mana abilities at almost any time you have priority, or even when you don't have priority but need mana to pay a cost (CR 605.3c). However, this is not "responding" — it is simply adding mana to your mana pool as part of paying a cost or while you hold priority before passing it.

Concrete example: Your opponent taps a Llanowar Elves for green mana. You cannot cast Shock in response to destroy it before the mana is produced — the mana is generated immediately, and no player receives priority between the tap and the mana entering your opponent's mana pool.

So the practical upshot: if you want to destroy a mana-producing creature before it can be used, you must do so before your opponent taps it, during a moment when you hold priority.