Can MySQL replace multiple characters?

You can chain REPLACE functions:

select replace(replace('hello world','world','earth'),'hello','hi')

This will print hi earth.

You can even use subqueries to replace multiple strings!

select replace(london_english,'hello','hi') as warwickshire_english
from (
    select replace('hello world','world','earth') as london_english
) sub

Or use a JOIN to replace them:

select group_concat(newword separator ' ')
from (
    select 'hello' as oldword
    union all
    select 'world'
) orig
inner join (
    select 'hello' as oldword, 'hi' as newword
    union all
    select 'world', 'earth'
) trans on orig.oldword = trans.oldword

I'll leave translation using common table expressions as an exercise for the reader ;)

Cascading is the only simple and straight-forward solution to mysql for multiple character replacement.

UPDATE table1 
SET column1 = replace(replace(REPLACE(column1, '\r\n', ''), '<br />',''), '<\r>','')