Horse Protection Amendments Act of 2014 - Amends the Horse Protection Act to replace the Designated Qualified Persons program responsible for inspecting horses for soring with a new inspection system. (The soring of horses is any of various actions taken on a horse's limb to produce a higher gait that may cause pain, distress, inflammation, or lameness.)

Requires a sore horse to be disqualified from being shown or exhibited for at least 30 days for the first determination that the horse is sore and 90 days for a second determination and any subsequent determination.

Requires the Secretary of Agriculture (USDA) to establish a single Horse Industry Organization (HIO) in order to establish a formal affiliation with the management of each horse sale, horse exhibition, and horse sale or auction, appoint inspectors to conduct inspections, contract with equine veterinary experts to advise the HIO Board on objective scientific testing methods and certification of testing results, and otherwise ensure compliance with the Horse Protection Act.

Directs the appointment of individuals by the Commissioners of Agriculture for Tennessee and Kentucky to govern the HIO. Requires those individuals to appoint individuals representing the Tennessee Walking Horse industry.