In the cell, division of mitochondria takes place on a regular basis, but what if there are no mitochondria present in cell (suppose all of them died), then can the cell make new mitochondria on its own?
If we were to suppose, as in the question, that all the mitochondria in a cell 'died' ('were irreparably damaged' would be better, as they are not independently alive) without any other consequences the cell would have no way of regenerating them. Even if the cell had another source of ATP (see @another 'Homo sapien' comment) such as anaerobic glycolysis, one very clear reason is that the mitochondrial DNA could not be replaced (there are no copies of it in the nucleus). If the mitochondrial DNA were not replaced, then there would be no way of making the mitochondrial proteins it encodes.
The cell would die for a more immediate reason than suggested in the comment, and one that should be of interest in relation to a less well-known function of mitochondria. Mitochondria play a key role in the process of programmed cell death — apoptosis. In this process signals cause the mitochondrial membrane to become permeable and allow the efflux of cytochrome c, which is a signal for activating the apoptopic pathway. Presumably if mitochondria were damaged by other means the leaching out of cytochrome c would have the same effect, causing the death of the cell.
If you think of the overall economy of an organism, it's often easier to make new cells rather than trying to repair ones that are beyond redemption.
Mitochondrial DNA: http://www.ncbi.nlm.nih.gov/books/NBK26924/
Apoptosis and mitochondria: https://en.wikipedia.org/wiki/Apoptosis#Activation_mechanisms