Large update and delete based on another table
A delete with an IN condition might be faster than the JOIN: 

delete from slave
where mid in (select master.id
              from master 
              where master.value in ('some', 'set', 'of', 'values'));

delete from master
    where value in ('the', 'same', 'set', 'of', 'values');


Another option that might be faster is to delete both tables in a single statement. This can also be used to delete multiple slaves.

with removed_master (id) as (
  delete from master
  where value in ('some', 'set', 'of', 'values')
  returning id
), remove_slave1 as (
  delete from slave_one
  where mid in (select id from removed_master)
)
delete from slave_two
where mid in (select id from removed_master);


This works as the foreign key constraints are evaluated when the statement is finished, not when each individual row is deleted. This has the additional benefit that you have to specify the "master values" only once.