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If I Use Plaguemaw Beast's Activated ability of "{t}, sacrifice a creature: Proliferate" and then target Vampire Hexmage with the activated ability of "Sacrifice Vampire Hexmage: remove all counters from target permanent", what happens?

Will Plaguemaw Beast force Hexmage to be sacrificed without being able to activate the ablity?

Will Plaguemaw Beast lose a valid target if Vampire Hexmage's ability is activated in response to sacrificed, so now Plaguemaw cannot Proliferate?

Will the Plaguemaw Beast's ability activate along with Vampire Hexmage's Activated ablity with Hexmage as a target?

Cascabel
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Austin
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    The duplicate I proposed explains this: you can't even activate both abilities as you're trying to. Sacrificing a creature is a cost for both abilities, and as the duplicate says, you can't sacrifice the same creature to pay for two abilities any more than you can use the same mana to pay for two spells. – Cascabel Jan 28 '16 at 03:20
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    As a side note, there's no targeting involved here. Neither of those abilities says "target", so "sacrifice a creature" never involves targeting. And things that you pay as costs aren't ever going to be targets. – Cascabel Jan 28 '16 at 03:45
  • @jefromi Hexmage's ability targets. It sounds like that's what he means. – GendoIkari Jan 28 '16 at 04:05
  • Though I at first read it as him using target incorrectly also. – GendoIkari Jan 28 '16 at 04:06
  • @GendoIkari Sorry, should've said there's no targeting in the way the OP said it - the question seems to talk about Plaguemaw Beast targeting, not the Hexmage. I understood that to mean targeting the thing to be sacrificed. – Cascabel Jan 28 '16 at 04:10
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    @jefromi It appears he uses "target" twice. The first time I believe he means targeting Vampire Hexmage with its own ability, which is correct.. But the. He does refer to plaguemaster losing a valid target, which as you point out is wrong. – GendoIkari Jan 28 '16 at 04:13
  • Ah gotcha, missed that. I'm not sure why you'd want to sacrifice your own Hexmage in order to remove all the counters from itself, but that's indeed what the question says! – Cascabel Jan 28 '16 at 04:18

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The question is a bit unclear. If you're trying to sacrifice the Vampire Hexmage to pay for its own activated ability, and to satisfy the Plaguemaw Beast, then no.

For each Plaguemaw Beast and Vampire Hexmage, the act of sacrificing a creature is a part of the cost of activating the ability. If you fail to be able to pay the cost, the ability will fail to resolve.

Drunk Cynic
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    "If you fail to be able to pay the cost, the ability will fail to resolve" is misleading. If you don't pay the cost, the ability will never be activated at all. – GendoIkari Jan 28 '16 at 03:23
  • @GendoIkari 602.2 details the process for activating an ability, following the process of 601.2. An object representing the activated ability will exist on the stack, costs are determined in 601.2.f, and the costs are paid in .2g and .2h. – Drunk Cynic Jan 28 '16 at 03:52
  • 602.2b says that 601.2 applies. "601.2i Once the steps described in 601.2a–h are completed, the spell becomes cast." Same for abilities. The ability is not activated until all steps are completed. You cannot activate an ability without paying its costs. – GendoIkari Jan 28 '16 at 04:00
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    You are right that it is on the stack when you pay the costs. But it hasn't been activated yet. And saying that it fails to resolve implies that it gets countered or something similar. – GendoIkari Jan 28 '16 at 04:02
  • Comes down to the joys of semantics. The process of 'activating' the ability puts it on the stack, and costs aren't yet paid. It isn't 'activated' until all requirements of 601.2 are met. The important measure is that effects that use the stack can't take place between the stated intention to activate the ability and the ability being activated. – Drunk Cynic Jan 28 '16 at 04:22
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    It is illegal to announce an ability that you cannot finish activating, so in a valid game of Magic, you will never have a case where you announce but fail to activate. So, it would be more accurate to say "If you are unable to pay the cost, then you cannot activate the ability". – murgatroid99 Jan 28 '16 at 04:39
  • @murgatroid99-They can commence activating the ability, until they've realized they can't pay the costs. At that point, 717 applies; the ability won't be activated, and play will be reversed. If this occurs repeatedly in a tournament, then Game Play Errors. – Drunk Cynic Jan 28 '16 at 04:55
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    717 is called "Handling Illegal Actions" for a reason. You're not actually allowed to partially activate an ability, but they provided 717 to give you a way back to a workable game state if you do break the rules. And the existence of 717 doesn't mean that illegal actions aren't Game Play Errors every time you commit them; it just gives a way for players to resolve them without calling a judge. – murgatroid99 Jan 28 '16 at 05:46