Muting Strings

I can't Figure out how to play the following:

G--12-12--11--7-7-7/9-
D---------------------
A--10-10--9---5-5-5/7-
E---------------------

Besides Plucking the strings with my fingers.
Is The only thing I can Do is mute the D string with my second finger? Any Help would be appreciated.

generally with something like that you need to pluck it. If you mute, you will get a funny muted sound in there, as I am sure you have discovered.

I pluck with my ring finger. It didn't take too long to get used to plucking.

Thumb and index finger. Thumb on the A string, index finger on the G string.

The way it's played depends on the way you want it to sound.
I play those kinds of "chords" alot, i fret it with my index and ring finger, and mute the string in between with my index finger. Then i just strum it like a chord.

Getting the string in between muted properly can be tricky. The extra sound you get from the muted note actually sounds pretty cool, a bit percussive-like .

trendkillah is right. On a lot of punk songs when they use octaves like that you are supposed to mute with your index so that in addition to the nice octave sound you get a little clang. However, if its classical music then you're probably supposed to pluck using your thumb and either your index or middle finger. Hope that helps.