Can I exit neet state counselling during 2nd round?If yes then what is the procedure?

Going by your profile we understand that you belong to Karnataka and hence this answer is being written in that perspective. If you are allotted a seat in Round 1, you have 4 options.

Option 1: You are happy with the seat allotted and you do not want to participate in further rounds.

Option 2: Satisfied with the seat allotted but wants to appear in subsequent rounds of Counselling. In such cases, you have to report to the College and pay the fees. But if you are allotted a better College, the seat allotted in the Round 1 will be automatically cancelled.

Option 3: Not satisfied with the Seat allotted and want to reappear for Counselling. For this, you need to rearrange your options during Choice filling.

Option 4: Not satisfied with the seat allotted and do not want to participate in further rounds of Counselling. In this case, the seat allotted will be cancelled.

If you have not been allotted a seat in Round 1 and want to exit, you just needn't participate in further rounds and the security deposit will be refunded after the completion of all rounds of Counselling. But if you have not been allotted a seat in Round 1 and you are participating in Round 2, there is no cancellation of seat option. You have to join the College failing which your security deposit will not be refunded.