Can an existing opening in a granite counter top be ground 1/8th inch to install new cooktop?

Of course it can. I could tell you exactly how to do this but it would be best if you would go to Home Depot and get thier opinion, thus making them the responsible one. You might wish them to do it since you have to ask this question anyway. It's all about hand held grinders with composite cut-off wheels etc,. etc,. Oh yes, safety gles, dust mask........you should really get someone else to do this for you.