Mazirek's last ability is a triggered ability, not an activated ability. It doesn't allow you to sacrifice a permanent whenever you want; rather, you need some other way of sacrificing permanents.

If you sacrifice a permanent as part of casting a spell or activating an ability, Mazirek's last ability will resolve before that spell or ability.

If you sacrifice Mazirek and other permanents at the same time, Mazirek's last ability triggers for the other permanents.

A legendary permanent that is put into a graveyard because of the “legend rule” isn't sacrificed.