Understanding the molecular mechanisms of neurological disorders is necessary for the development of personalized medicine. When the diagnosis considers not only the disease symptoms, but also their molecular basis, treatments tailored to individual patients may be suggested. Vitamin-responsive neurological disorders are induced by deficiencies in vitamin-dependent processes. These deficiencies may occur due to genetic impairments of proteins whose functions are involved with the vitamins. This review considers the enzymes encoded by the DHTKD1, PDK3 and PDXK genes, whose mutations are observed in patients with Charcot–Marie–Tooth (CMT) disease. The enzymes bind or produce the coenzyme forms of vitamins B1 (thiamine diphosphate, ThDP) and B6 (pyridoxal-5′-phosphate, PLP). Alleviation of such disorders through administration of the lacking vitamin or its derivative calls for a better introduction of mechanistic knowledge to medical diagnostics and therapies. Recent data on lower levels of the vitamin B3 derivative, NAD+, in the blood of patients with CMT disease vs. control subjects are also considered in view of the NAD-dependent mechanisms of pathological axonal degeneration, suggesting the therapeutic potential of vitamin B3 in these patients. Thus, improved diagnostics of the underlying causes of CMT disease may allow patients with vitamin-responsive disease forms to benefit from the administration of the vitamins B1, B3, B6, their natural derivatives, or their pharmacological forms.