Target removal & the stack

[Empathie]

 Can I destroy {Fulminator Mage} before its ability resolves if I put the removal after its activation, and Essentialy negate its effect?

[Keyeto]

You cannot. Sacrificing the Mage is the cost to activate the ability. By the time you can respond, it's already in the graveyard, and the ability is on the stack.