If you are refering to what I think you are refering to, it is called pinch harmonics and you are doing it right, but to heavily.
You put the pick below the string and your thumb above with only a little bit of the pick sticking out. Then you twist downwards so that your thumb picks down and the pick picks up.
You have gotta practice it or else it will just mute the string like you said.
It is easy after a while.

If this does'nt help try looking at the techniques lessons on this site.