The Fourteenth Amendment says "nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws." Note that it refers to "person[s] within its jurisdiction"  rather than citizens. Non-citizens, whether legal or illegal, don't have all of the rights of citizens, but they are protected by portions of the Constitution that Arpaio violated, including the Bill of Rights.