What would happen to skin cells if mitosis did not take place?

If mitosis did not take place, the skin cells would die and they do not get substituted. The skin cell divides briskly so that to maintain a protective barrier against infection. The epidermis is the outer layer of the skin and comprises majorly of dead cells, which constitute keratin.  

Keratin refers to a tough fibrous protein found in the skin, hair, and calluses, and functions as a protective covering. The epidermis cells are spontaneously going through the process of mitosis so that the outer dead cells comprising keratin get briskly substituted as they fall off.  

Afterward, the newer thriving cells start generating keratin, lose their cellular constituents and die, and thus, the cycle goes on. The skin functions as a protective layer to infection, thus, it is renewed and repaired spontaneously.