does 'cutting' here just refer to the slicing of meat? or can it also mean a reduction in consumption?
Cutting like slicing with a knife, not reducing (e.g. the consumption).
Is it possible to leave out the article "the" in examples like this?
Yes, of course.
Creamy (kroimy) red meat!
Doe this mean red meat like beef and pork like it does in English (as opposed to white meat like chicken)
Yes, as far as I understand "czerwone mięso" includes veal (cielęcina), beef (wołowina), pork (wieprzowina) and mutton (baranina).