What is the criterion that makes a particular drink fall under the category of forbidden (haram)? Is it solely that it completely intoxicates the mind?

The basic principle regarding beverages is permissibility. What is prohibited among them is that which is intoxicating, or causes stupor, or is harmful to the body, due to the Prophet's (peace and blessings be upon him) prohibition of every intoxicant and stupefacient, and due to the Hadith: "There should be no harm nor reciprocal harm." Tea and coffee are neither intoxicating nor stupefying, so they are among the permissible beverages. As for smoking, it is prohibited due to the harms it contains, and stimulant and sedative pills are prohibited due to the harms and dangers they contain.