"I want food without meat."
Translation:Θέλω φαγητό χωρίς κρέας.
Because "κρέας" is considered to be "τροφή" by itself.
The issue of "τροφές" and "φαγητό" in greek is almost like the issue of "foods" and "food" in english. 'Food' is a non-countable noun when it refers to food in general. When discussing specific foods, for example, different national cuisines, or a listing of various foods in a person's diet, (a type of food), 'foods' is countable.
Τροφές = foods
Φαγητό = food
Meat could actually be a food in a person's diet, so it's considered "τροφή", and could be contained in food (φαγητό).
It's pretty tricky to explain, but I hope I helped you enough. ^.^