Why would mussels be gritty?
With regards to the grit, if they aren't farmed mussels (which generally are fairly clean) you may want to give them a soak for a while. This will give them the chance to expel any further sand/grid they may contain. There are varying theories of whether to use tap water, salt water, sea water or various other concoctions. And admittedly there are those who say any form of soaking will do all sorts of harm to the flavour. But if the alternative is disappointing gritty mussels, why not give it a try. 

And as always, ask your fishmonger for advice. They will know the origin of the product, and whether or not you need to take extra steps in preparing them. 

As for discarding opened mussels, don't just discard them when they seem open on arrival. If the shell is not cracked, give them a light tap (on the counter or with a knife) and see whether or not they will close in response. If they close in response, they are fine. If they don't close or tell you to stop it, then discard them. 

And if two thirds of the batch really are dead ... I personally would not necessarily trust the other third to be in great shape.