Does Stifle work on mana abilities?

Stifle counters a targeted activated or triggered ability on the stack. The critical issue is that mana abilities never go on the stack at all — they resolve immediately when activated or triggered (CR 605.3b). Because Stifle requires a target on the stack, it simply has nothing to target when a mana ability is used.

A mana ability is defined as an activated ability that could produce mana, is not a loyalty ability, and does not have a target — OR a triggered ability that could produce mana and triggers from another mana ability (CR 605.1). The moment you tap a Llanowar Elves or similar permanent for mana, the mana goes directly into your mana pool with no window for Stifle to interact.

Stifle's oracle text reads: 'Counter target activated or triggered ability.' Because mana abilities are explicitly excluded from the stack by CR 605.3b, they are never legal targets for Stifle, regardless of timing.

Concrete example: Your opponent taps their Sol Ring to add {C}{C} to their mana pool. You cannot cast Stifle in response to stop this — the mana is already in their pool before anyone gets priority, so there is no ability on the stack to target.

Note: Non-mana activated abilities that happen to produce mana as a side effect (e.g., Goblin Sharpshooter's ability if it somehow produced mana) would still use the stack normally and could be Stifled. The key is whether the ability meets the CR 605.1 definition of a mana ability.