Can I avoid having bad grades and a dismissal show on my record if I transfer colleges?
Graduate schools generally ask for all of your undergraduate transcripts, not just transcripts from schools you got a degree from.
Transferring is a decision you'll have to make on your own, but it is probably not a mechanism to clear your record of Ws if that's your intent.
In the meantime, probably best to focus most of your attention on your mental health, followed by graduating itself, regardless of future plans past then.