When downstriking , use the part of the palm near your picking hand's thumb to mute the lower 4,5,6 strings , and lay your fretting hand on the higher strings to mute.
When upstriking , use your picking hand free fingers (pinky,ring & middle) to mute the high e, and b strings after picking them or keep your fretting hand fingers just touching the string to mute .
Make sure that moving from a string to another should be smooth.
With these particular 3 string sweep , you should pull-off from 19 to 15 ... And same with sweeeps that have exact similar pattern.
Pick like this:
...D..D..D...U.......U..U
E--------15--19-p-15---------
B-----17-------------17------
G--16-------------------16---
There are millions of ways to mute , try them all and practice the ones your most comfortable with ... When playing , you shouldn't be thinking of muting at all , it should come natural (after lots of practicing of course).