How to resign immediately to join a new employer?

Dear sir/madam,

I am working on a mission visa in the UAE. I got another offer from another employer. They require to join immediately. But my current employer does not give a release immediately.

They are saying that 1 month's notice period is required. Is a notice period required for a mission visa?

And if I miss that offer, can I file a case against the current employer?

Please advise!