Countering the spell or ability will not save Phantasmal Dreadmaw from being sacrificed.

If Phantasmal Dreadmaw becomes the target of a spell or ability, its ability triggers and goes on the stack on top of that spell or ability. Phantasmal Dreadmaw will be sacrificed before that spell or ability tries to resolve. Unless the spell or ability has another target, it will then be removed from the stack as it tries to resolve for having no legal targets.