Plague Boiler
At the beginning of your upkeep, put a plague counter on this artifact. {1}{B}{G}: Put a plague counter on this artifact or remove a plague counter from it. When this artifact has three or more plague counters on it, sacrifice it. If you do, destroy all nonland permanents.
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Official rulings (3) · Scryfall
You choose whether to add or remove a counter when the second ability resolves. You can’t choose to remove a counter if there isn’t one there.
If the third ability triggers, removing a counter in response won’t stop the effect. However, somehow removing Plague Boiler from the battlefield in response would stop the effect because then you wouldn’t be able to sacrifice Plague Boiler.
The sacrifice is done on resolution of the triggered ability.