If a dietary supplement claims to cure, mitigate, or treat a disease, it would be considered an unauthorized new drug and in violation of the applicable regulations and statutes. As the FDA states, in a response to this question, in a FAQ:
Is it legal to market a dietary supplement product as a treatment or cure for a specific disease or condition? No, a product sold as a dietary supplement and promoted on its label or in labeling* as a treatment, prevention or cure for a specific disease or condition would be considered an unapproved--and thus illegal--drug. To maintain the product's status as a dietary supplement, the label and labeling must be consistent with the provisions in the Dietary Supplement Health and Education Act (DSHEA) of 1994. *Labeling refers to the label as well as accompanying material that is used by a manufacturer to promote and market a specific product.
Dietary supplements are permitted to make structure/function claims. These are broad claims that the product can support the structure or function of the body (e.g., "glucosamine helps support healthy joints", "the hormone melatonin helps establish normal sleep patterns"). The FDA must be notified of these claims within 30 days of their first use, and there is a requirement that these claims be substantiated. In reality, misleading claims about supplements are common, particularly on poorly regulated commercial websites. For example, the compound hydrazine sulfate is sold as a dietary supplement in the USA and promoted as a treatment for cancer, despite little evidence that it is either safe or effective.
Other claims that required approval from FDA include health claims and qualified health claims. Health claims are permitted to be made if they meet the requirements for the claims found in the applicable regulations. Qualified health claims can be made through a petition process, including scientific information, if FDA has not approved a prior petition.