REPLACE does a good simple job of replacing characters or phrases everywhere they appear in a string. But when cleansing punctuation you may need to look for patterns - e.g. a sequence of whitespace or characters in the middle of a word or after a full stop. If that's the case, a regular expression replace function would be much more powerful.
UPDATE: If using MySQL version 8+, a REGEXP_REPLACE function is provided and can be invoked as follows:
SELECT txt,
REGEXP_REPLACE(REPLACE(txt, ' ', '-'),
'[^a-zA-Z0-9-]+',
'') AS `reg_replaced`
FROM test;
See this DB Fiddle online demo.
PREVIOUS ANSWER - only read on if using a version of MySQL before version 8: .
The bad news is MySQL doesn't provide such a thing but the good news is it's possible to provide a workaround - see this blog post.
Can I replace or delete multiple strings at once? For example I need
to replace spaces with dashes and remove other punctuation.
The above can be achieved with a combination of the regular expression replacer and the standard REPLACE function. It can be seen in action in this online Rextester demo.
SQL (excluding the function code for brevity):
SELECT txt,
reg_replace(REPLACE(txt, ' ', '-'),
'[^a-zA-Z0-9-]+',
'',
TRUE,
0,
0
) AS `reg_replaced`
FROM test;