How do i take off the chevy emblem off of the grill of my blazer so that i can paint it and put it back on?

I believe, for the 96 and later, it is just held in with adhesive. A little heat will help in the removal process.

If you are just looking to paint it, why not mask the grill off and paint it in place?

In some models u may hav to undo a bolt in the back i believe

On mine it was bolted on.
Don't know what year you have, but i know on 98+ you have to take off the grille (be careful doing this though) and then remove the nuts from behind the emblem.

Or do like swartlkk said and just mask around it...

mine is bolted on too, and since the grille is held on with clips, if any have rusted it can turn into a not fun time. like everyone else said, just tape it off and paint it