The short answer is: not likely. The long answer is that if you search really really hard and find a new sink with either the exact same cutout (unlikely) or a larger cutout, you can maybe get a granite fabricator to do it. BUT, they likely won't warrant "shaving" off such a small amount of granite without potentially breaking the slab.

It depends on a few things.
If the sink is epoxyed to the countertop you're going to have a rough time separating them.
If the sink is siliconed to the countertop it'll be easier to separate the two.
You'll need to make sure that the sink flange is clear of the interior cabinet walls so that once separated, the sink will be able to drop into the cabinet.
Also, as "hollysprings" said you need to figure out if your cutout will accommodate your new sink.
So, it may be do-able but you'll need some luck on your side.

We were told when we bought our undermount sink in our Formica countertop, that if we ruined the sink somehow, it could be replaced by a surface mount sink. Maybe check with a plumber.

Hello Janesylvia, In most cases an under mount sink can be changed. As mentioned above, the easiest way is to use a top mount sink. I had a customer call yesterday looking for a specific size sink to replace his existing sink. I did a Google Image Search using the dimensions required and a description of the sink and found him a sink in less than 3 minutes. He had been looking for days. Maybe you could try doing that.