If a permanent is sacrificed to pay a cost of a spell or ability, Mazirek’s ability will resolve before that spell or ability. Conversely, if a permanent is sacrificed during the resolution of a spell or ability, that spell or ability will finish resolving before Mazirek’s ability is put onto the stack.

Mazirek itself doesn’t allow any player to sacrifice any permanents. Its ability triggers whenever a player sacrifices a permanent because some other spell, ability, or cost instructed the player to do so.

A legendary creature that dies because of the “legend rule” isn’t sacrificed. The same is true for a planeswalker that is affected by the “planeswalker uniqueness rule.”