The meaning of 'cut out' in this sentence = ill-suited ( not suitable) or fit to be something due to one's nature . I cannot stand the sight of blood . Now you know why I am not cut out to be a doctor. I am not cut out to be an artist ,because ,by nature ,I am not a creative person .

"Cut out" in this sentence means "fit" or "meant". "I wasnt meant to be a doctor" and "I wasnt cut out to be a doctor", mean the same thing.