The main diet of the blue mussel is microscopic drifting organisms which are collectively called   plankton  The mussel sucks plankton through the inhalant siphon or intake tube.   The gills are designed to more or less strain out the plankton (actually it is a little more complicated than this but we won't bore you with the details).  The waste water then goes out the exhalent siphon or exhaust tube.  In the meantime the food is transported to lips next to the mouth. 

Inhalant & Exhalant Siphons

Some plankton [such as the dinoflagellate to the left] contain a poison.  When they reproduce very fast, the red pigment in the plankton turns the water red [some red tides].   

Since mussels filter large volumes of water and are immune, they can accumulate the poison.  It is strong enough to kill a person eating even a few mussels under certain conditions.