If you sacrifice a creature to pay a cost, can its leaves-the-battlefield triggered abilities be responded to before the spell or ability resolves?

When you cast a spell or activate an ability, costs are paid as part of the process of putting that spell or ability on the stack (CR 601.2h for spells, CR 602.2 for activated abilities). No player receives priority during this payment window, so no one can respond to the sacrifice itself mid-payment.

Triggered abilities that trigger during the payment of a cost — including any 'leaves-the-battlefield' triggers from the sacrificed creature — are placed on the stack only after the current spell or ability has been fully announced and placed on the stack (CR 603.3). They wait in a 'trigger holding zone' until the next time a player would receive priority.

In a typical sequence, the triggered ability from the sacrifice does not go onto the stack until after the original spell or ability is already on the stack. Both players then receive priority with the original spell on the stack first. The triggered ability is put on the stack on top of it, meaning the trigger actually resolves before the spell or ability that caused the sacrifice does.

Example: You activate Viscera Seer by sacrificing Solemn Simulacrum (triggering Simulacrum's 'leaves-the-battlefield' draw ability). Viscera Seer's scry ability goes on the stack. Then, before anyone can respond, the Simulacrum trigger is also put on the stack on top of it. Your opponent can now respond to the Simulacrum trigger, but they cannot 'undo' the sacrifice or respond before the scry ability was placed on the stack.

Key rules: CR 601.2h (paying costs when casting), CR 602.2 (paying costs when activating), and CR 603.3 (triggers wait until the next time a player would receive priority to be placed on the stack).