When we pulled out our kitchen backsplash we just pulled out the damaged drywall as well, put new in, and tiled over that. It's simpler than trying to clean off the old gunk, and drywall is cheap and easy.

Green board would be overkill, even behind the sink. Regular drywall is fine.

Sorry I'm posting so late, I've been away for several days.

What weedy wrote.

The more translucent the glass, the more what is behind the glass can show through.

Add to that with mosaic you want flat as flat can be so the tiles don't rock this way and that.

So I'd cut out whatever crappy mastic board there is, then use regular drywall. Use a white thinset to set the glass.

Thanks so much to both of you, Working on it now......out with the old....love it..