It's all in your fret hand. Don't concern yourself with trying to palm mute, you can mute the strings with only your fret hand, and it won't give you that choppy-click every time you hit a note. That doesn't mean hold your pick hand off the strings, just don't palm mute, and concentrate more on releasing the notes to make them sound clean and not ring out.

inb4 Makemetalmusic has no idea what he's talking about.

ive done that twice, hardly "always"

and its because hes kinda wrong. well what he is talking about is correct, but you have to palm mute also. not palm muting properly is one of the most common problems people have when learning sweeps.

face palm

this is what we all fucking mean man

Do it slowly.

pick each note one by one (obviously in the sweeping motion) it will come.

thats your choice dont matter