The answer is yes, you should be able to replace the sink under certain circumstances.
Do you know if your granite thickness is 3 centimeters thick (approximately 1-3/16″), or is it 2 centimeters, with a laminated drop edge?
Do you see a seam on the edge? The reason I ask is that in some cases where you have a 2cm laminated countertop there is an underlayment plywood sub-top installed on top of the cabinets and sometimes a stainless steel sink lip is supported by the sub-top. This creates a sandwich effect where the lip of the sink is locked in between the plywood subtop and the granite.
In most cases, the sink is supported either by wood supports or there may be clips which are drilled into the back of the granite and the sink is “hanging” by the clips.
The best thing is to look from the underside and see if you see plywood supporting the sink or clips.
If there are clips then the sink usually can be removed by loosening the fasteners, heating up the sealant between the the sink and the granite with a heat gun and with a stiff putty knife, cutting the bond between the granite and the sink. The sink should drop out the bottom. Most sinks can then be turned sideways and pulled up through the cutout hole. If the sink is particularly large it sometimes is supported by the side cabinet partitions. This can be a problem and would require that you cut away part of the partition to remove sink.
I think a bigger issue is to get a stone fabricator who is willing to do this kind of a retrofit. In some markets, this is just too fussy of a job and many fabricators shy away from such projects. You may be lucky and find someone who is willing, but make sure they are reputable. Check references, etc.
The process of cutting the revised sink cutout is fairly standard and easy. Most fabricators can do this on site, although it can be messy.
Ask if they have dust collectors and how will they control dust and mess. You should be able to find a sink that will accomodate your faucets, sprayer, etc. A great source for high quality sinks (composites included) is Mr. Direct. We use them all the time:http://www.mrdirectint.com/
If you have any more questions, feel free to reply. Take pictures above the counter and inside the sink box (cabinet) looking up at the bottom of the sink.