Your offer letter states 2 months notice but you are only giving your current employer 2 weeks. As you can see yourself its not justified.

He cant reject your resignation letter but you are required to serve the notice.Is there any salary in lieu option? If there is you can opt to pay the company the remaining outstanding notice.

Companies generally wont sue but one could never say never.

This is depending on your HOD/HR discretion. You cant say he can, why me cannot? It does not work that way.

Suggest you to try talking with your superior again.