I mute with both my left and right hands while playing. If you have harmonics and buzzing with sweep picking, then your problem is most likely in your left hand muting. Having a really hot guitar output, or if you've kicked up the overdrive heavily on your amp, then you'll have more trouble properly muting the notes, but what it amounts to is practice that you need. Go really slowly and examine exactly where the problem lies. Once you fix it, you'll be able to play the same passage fast smoothly, but as a general rule, if you can't play it well slow, then you probably won't be able to play it well fast.