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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”

An ability that triggers whenever a permanent “is tapped for mana” or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

You can't remove cards from the draft that you've already drafted. Only cards drafted after you draft Cogwork Grinder may be removed this way.

No other player may look at the cards you remove from the draft (unless Cogwork Spy allows a player to).

If a Cogwork Grinder owned by another player enters the battlefield under your control, the number of counters it enters with will be based on the number of cards you've removed from the draft with Cogwork Grinders, not the number its owner removed. Unless you also drafted Cogwork Grinder, this will be 0.

If you draft multiple Cogwork Grinders, the value for X will be the same for each of them. It doesn't matter that some of the removed cards may have been removed before you drafted the second Cogwork Grinder, for example.

A card that is removed from the draft isn't in any player's card pool. That card can't be played in any games associated with that draft.

You still draft the card that you remove. This may matter if an ability refers to "the next card you draft" or similar. If that card instructs you to draft it face up, do so, then turn it face down as you remove it. If that card instructs you to reveal it as you draft it and then perform additional actions, perform those actions before turning the card face down and removing it from the draft.