No, you can't do that.
Casting a spell follows this basic process:
- The player puts the card on the stack.
- They make all choices for that spell, including targets, additional costs, etc.
- They pay for the spell.
During this process nobody is allowed to cast spells, activate abilities, or do anything at all really — the exception is that the player can activate mana abilities while casting their spell to pay for it.
Only after this process does any player gain priority, meaning they are allowed to cast spells and activate abilities. The player who cast the spell gets priority first, then they can pass priority to the next player in turn order, and so on. (For more details on casting spells and priority see In plain English, how does casting spells and using creature abilities work with the stack and priority?.)
This means that by the time you are able to cast spells in response to your opponent casting Molten Disaster, it has already been fully paid for. It is too late to tap down their lands. Plus their Molten Disaster is now on the stack with split second so you can't cast spells at all until it resolves!
If you did want to tap down their lands, they can just activate them for their mana in response anyway while your spell is still on the stack, and use that mana right afterwards.
No, you can't. When your opponent announces that they're casting Molten Disaster, you can't do anything until the moment it's already on the stack and it's paid for with mana obtained by tapping lands. It doesn't really matter if it has split second or not.
Since Molten Disaster is a sorcery, one thing you could do is casting Mind Games during their upkeep (or draw step). They would have to wait until the main phase before they can cast sorceries, and mana pools empty at the end of each step and phase. Of course, this would assume you know they have Molten Disaster (e.g. via Telepathy) and not enough lands to cast it otherwise.
Other answers have mentioned that mana abilities can be activated during the casting of the spell, and there's no time for the opponent to react in between.
But even if mana abilities weren't special, but worked at instant speed like almost every other ability, you still couldn't prevent an opponent from casting a spell by tapping their lands in response.
Consider some non-mana ability that has a cost of tapping the permanent in question, e.g. Soulmender, which has "Tap: You gain 1 life."
Tapping Soulmender is part of the cost of that ability, and it happens immediately when the player announces the ability they are activating. The cost is paid, the ability goes on the stack, and priority goes back to the same player. Rule 602.2:
602.2. To activate an ability is to put it onto the stack and pay its costs, so that it will eventually resolve and have its effect.
If the opponent casts a spell or activates an ability that taps Soulmender in response (when they get priority), it wouldn't have any effect: the cost would already have been paid when that spell/ability resolved.
Similarly, even if you could cast Mind Games between the opponent tapping their lands and casting the spell, the cost of tapping the lands would already have been paid once it resolved.
(If all mana production worked at instant speed, it would allow some other tricks, though.)
I'm guessing you asked specifically about a spell that has split-second because you understood split-second as:
You can't cast spells unless they're mana abilities. You can use abilities unless they're mana abilities.
Where you consider Mind Games to be a "mana ability" because it taps lands.
But split-second actually means:
You can't cast spells. You can't use abilities unless they're mana abilities.
A spell, whether it taps lands or produces mana, is not a mana ability. "Mana ability" refers specifically to activated abilities and not spells. A mana ability is an activated ability that produces mana in addition to its other effects.
See the other answers for why you can't counter a spell by tapping the lands that would be used to cast said spell.