It's funny, I asked the same question when I first noticed this. But I'll be the first to tell you: any guitarist who plays rock, blues, or especially metal has this issue. In fact, that's why good guitarists spend time perfecting their muting ability.

Now, when you're picking across strings while ascending (going from the low E string towards the high e string), it's easiest to mute these open strings because you can just use palm muting or even your picking hand thumb (like I do) to mute these lower strings after you're done playing them. And these lower strings will be much more noticeable than the thinner strings when they're ringing out after you pull off (not a pull-off, I mean when you're taking your finger off). So it's important to perfect your palm muting or thumb muting technique.

Now when you're descending (going from the thinner strings towards the lower thicker strings), you can't exactly mute them the same way. You'll either have to use your fretting hand fingers to mute by laying them flat over the strings, or you can use you picking hand fingers and literally place your extra fingers on these strings. But honestly, you don't have to worry about these higher strings as much, because they're not too noticeable when they're ringing out.


So whatever method you choose, just take some time to play really slow and really think about the best way to mute these strings. Expert guitarists spend more time perfecting this than you would think. They all deal with these open strings ringing.

And the reason I mentioned metal, rock, and blues is because these styles are usually played with lots of gain, and that's when this string ringing is most noticeable. If you play with a clean, acoustic tone from your amp, this ringing is hardly even noticeable.

I hope that helps!

~Rusty