I know I can order food using phrases like 我(想)要／请给我一份...
But how would I exclude an ingredient, e.g. if I don't like garlic?
Would any of those be correct?
Any of these sentences would be grammatically correct. However
would be a better and more common usage in my opinion.
It would be even better to include the character in the parenthesis,
which means "add" or "with" or "include".
if you are speaking Cantonese, you can use
in English it's something like take it off.
我要一份青椒肚片不 放 蒜。
我要一份青椒肚片 别搁 蒜。 (more intensive than 不搁)
I think 放，搁 sounds more natural and navtivelike.