What could be the underlying illness of cuts on my foreskin?

Probably phimosis: Phimosis or tight foreskin can result in minor splits in the foreskin whin it is retracted, these may mimic "cuts". You may require circumcision, or steroid cream. Consult with a urologist.

Balanitis?: It may be that your foreskin is just too tight; but it could also be balanitis, a skin condition affecting the head of the penis. This is not necessarily a sexually transmitted disease. It may be due to a fungal, bacterial, or yeast infection.Wash the area right after sexual activity with a mild soap and apply a moisturizing cream. If the problem persists, see your doctor.