I've just started to learn sweep picking from the Justin Sandercoe mini arpeggios vid. I have the action all right and im slowly picking up speed, but i've started to notice that when I lift my finger off of the 13th fret of the B string, I can hear the the open B ring out. How can I best deal with this?
Quote by griffRG7321
Learn how to mute unwanted strings with your palm.

This, but it can also be because you're so close to the 12th note harmonic. Try moving the arpeggio around and see if the problem persists.
But how can I mute a single string without first muting eitehr one of the others or the note that I wanted?
Guitar Techniques forum. This is largely a music theory forum. You generally get better results when you ask the correct specialists.

OT: I don't know the chord shape you're playing, but I either mute with my left hand (using an unused fingertip or the side of my index finger) or skip the string entirely.

Rereading your post, it looks like you've got a simple problem of removing your finger without making string noise. That's just something you acquire with proper practice.
Quote by SonOfPest
Its the Lydian mode; formed in Eastern Arabia when the Persians invaded England.

Quote by Blind In 1 Ear
try the sexolydian scale.