If bacteria with recombinant DNA molecules do not survive in gene cloning, how they can be grown into a colony after being isolated?
The question confuses too many things. The process being described, Lac Z Blue-White Screening, doesn't involve cutting the ampicillin gene, nor do the bacteria with the recombinant DNA or without the recombinant DNA die in the process of the experiment.

The plasmid contains a Lac Z gene involved in creating enzymes that break down galactose. In a test tube, the vector plasmids take up the gene of interest and the recombinant DNA is produced. The recombinant DNA is then added to the medium of bacteria, but only some of the bacteria will be transformed and take up the plasmid vector. In these bacteria, restriction enzymes will 'cut open' a space for insertion in the Lac Z gene, and DNA ligase will seal it up. The insertion of the gene in a bacterium disrupts the Lac Z gene and make it unable to produce the required enzymes to break down galactose. Then, the bacteria are applied to a Petri dish that contains growth media with a derivative of galactose, X-gal in it. When X-gal is broken down by the bacteria able to create the necessary enzymes from their functional Lac Z genes, the bacterial colony will turn blue. So, when you add these bacteria into the Petri dish, only the bacteria without the recombinant DNA will break down X-gal and turn blue, whereas bacteria with the recombinant DNA will not be able to break it down and remain white. This allows the researcher to distinguish between the bacteria with and without the recombinant DNA, and allow them to isolate for the ones with it.