Ask to serve notice period and cannot by-out

Hi Sir, I would like to tell you that I got another opportunity in a new company and they are asking me to join within 15 days. So i put a resignation mail with my manager, HR in loop. Today I got a call from HR and she said that the company has 60 days notice period and I have to serve it and can ask my new company that it will take 60 days to join. Further i asked her that I am ready to buy-out my notice period which was mentioned in the offer letter too as “ After successful completion of probation and having been confirmed in writing, either party to this Agreement may terminate the same, even without cause by serving a notice in writing to the other and providing 60 days’ notice or on making payment in lieu thereof.” , but HR said by-out is not an option and i have to serve notice period. Though i worked in this company for 10 months and still not got any confirmation letter yet. My question is that what should i reply to HR regarding this as by-out is mentioned in appointment letter. My resignation was effective from 17th September,2021 and i have to join new company on 4th october,2021. Please guide