how do you play chords that skips strings? do I just mute them or really physically skip them?

example this chord

Two ways:

1) Mute the intermediate string (D in this case) with a finger on your fret hand
2) Hybrid pick, i.e. use a finger on the pick hand to pick the string after the skip (G)

I think option 1 is the most common (and easiest, especially if it's a fast song).
yeh, you just have to mute it with whatever finger you end up feeling will do the job best