Is it safe to drive a car if constant velocity joints need replacing fiat punto?

It is safe until one of them breaks, and that could happen at any moment. If I were you, I'd make sure you have a good pair of walking shoes, if you don't get it fixed you've got a long walk ahead of you. If that joint should break, the car isn't going to go anywhere. That car needs two axles to make the car go and if one is broken or missing, the transmission will just spin. It is possible that a wheel could lock up, but I don't think it's very likely, but do you want to chance it? Can the failure of the joint possibly cause other damage to the car? Yes it will. If it breaks at highway speed the damage could be considerable. I have seen broken shafts rip out oil pans, brake lines (no brake line, no brakes) and crack transmissions. I would highly recommend getting it fixed as soon as possible.