After purge mussels 6 time in salt water 20 mins each, why they still exude much grime?
If your mussels are really that dirty, scrub them well first, then soak them in fresh water + salt (about 35g per litre) - or sea water - and add a scant handful of ground oats. The oats are supposed to irritate the mussels and they'll purge it together with the sand, while the salt water will keep them alive.

It can take a long time to purge really gritty mussels (according to some sources, from 2 to 12 hours). I'm not sure how clean you expect your mussels to be, just make sure most of the sand is purged.

You should also ask the shop if the mussels have been purged before - it's usually the case.