Destroying an Artifact

[An Angry Fatman]

{Thoper Assembly Line} is activated and responded with a {Rakdos Charm} would it still resolve?

Edit: {Thopter Foundry}

[An Angry Fatman]

{Thopter Foundry} sorry

[redwolv]

Yes, the ability will still resolve.

[An Angry Fatman]

Why would it? If {Olivia Voldaren} is on field and you ping a creature, then responded with a {Dismember} would the creature still take one point of damage?

[Kaylesh]

Why would it? If {Olivia Voldaren} is on field and you ping a creature, then responded with a {Dismember} would the creature still take one point of damage?

Yup. Once you activate the ability, it exists on the stack regardless of it's source.

{Thoper Foundry} is activated and responded with a {Rakdos Charm} would it still resolve?

If you destroy the foundry, the ability will still resolve, because what was mentioned before.

If you're looking to destroy the artifact that was sac'ed to prevent the paying of the cost: you can't. That artifact has been gone before you receive priority to cast your charm.