How to play dirty-clean???

Hy there!
I play guitar for nearly 4 Years, but if I want to play some faster Stuff (I only use half gain on my Boost-Channel) it sounds like soupe.
I tried to hold the Strings, which shouldn't swing with my the fingers of my right hand, but it's nearly impossible to hold the b-String without muting the other ones.
Is there a trick or is it "just" training?

You'll get it eventually. It's mostly a matter of building up the strength and flexibility to do what you want to do without mashing all of the strings down in the process.

Also use you palm to mute the strings, Playing clean lines is a time consuming technique, basically, it's the one you work on all your life, since a new line will never be clean... When you can play what you hear in your head instantaneously, AND cleanly, then you're a master...