You should try to sweep without palm muting any strings that you play, otherwise you will not be able to produce a fluid and open sound. In your example, you should palm mute the E and A strings because they are not used. Note, however, that this doesn't mean that your picking hand is totally fixed to the bridge. It should be able to move freely, which can be achieved if your palm touches the low strings only lightly. The muting of the other strings can be achieved in two ways.
The first is to mute the strings with your fretting hand. This means that as soon as you've played a note, the corresponding finger releases the pressure but it stays on the string for a moment such that the string is muted before the next string rings. Furthermore, the tip of the finger playing the next note can mute the lower string.
In your example you play the first note with your third finger. Then you release the pressure and use the third finger to mute the d string. The next note is played with the first finger on the g string. You can fret that note in such a way that the tip of the index finger mutes the d string. In this way, you mute each string twice, which makes sure that it doesn't ring out longer than it should.
The other approach for muting is using the thumb of your picking hand. The thumb needs to be almost straight and the inside of the thumb touches the strings while you sweep, of course only the strings that are lower (in pitch) than the one you're picking at the moment. In this way you can also achieve very clean sweep sounds.
I think that most people use some combination of these two approaches. As usual, it is important to try everything, and do everything very slowly to figure out what works best for you.