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there's a couple different mute techniches.
Palm Muting, usually noted as "P.M............" in tab over the section is as above.... resting the picking hand forward of the bridge on the strings so that the strings do not "ring out" (think like in a piano -- the pedals. )
now, killing in the name, has some almost like "scratching" muting going on
with your fret hand, kinda just rest your hand over the strings and pick them almost like a full strum of an open chord, but with more force.