You should not mute the notes you're playing like aiwass said , only unplayed strings should be muted to make one note sound at a time , however you can mute them all on purpose if desired.

Muting techniques are very complicated to explain or even to watch (I drool when I look at my playing to analyze my muting technique ;) ) , but it's very easy practically & should come very natural and without having to work your mind very hard , sometime you'll find your fretting hand doing the muting job exclusively , other times you'll need help from your picking hand ... I'll try to summerize the muting thing for you :

A) Fretting hand muting :
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1) Thumb : For Lower strings (basicaly lower E string)
2) Laying your fingers on higher pitched strings.
3) Touching the Lower (in pitch) adjacent string with a fretting finger.
4) Using your index finger to lay on all strings (specificaly lower one's) , while normaly playing with other fingers ... ( This one isn't for sweeping in general , but I think it might help)


B) Picking Hand muting :
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1) Palm : As you normaly Palm Mute , but you should also try to use this to ONLY mute UNPLAYED strings.
2) Free fingers : If you hold your pick between index and thumb , you'll have three fingers free for muting purposes.


I also recomend to practice sweeps with clean tone first to make sure you're not messing at any point and that everything is clear , then take care of the muting with little distortion and increase distortion gradualy till your can sweep clearly with a DeathMetal tone.