“채식”(菜食) means “living on vegetables” and “주의”(主義) means “a principle“ or “a policy”. “자”(者) means “a person”. To describe “a vegetarian”, this word(채식주의자/菜食主義者) is very similar to the Mandarin(素食主義者)
Hope it helps.
Did you noticed this sentence is informal and while talking informal you don't say respected words like Mr.or Mrs or anything ,So putting Mr.garam is wrong instead use garam.
Mr./Miss./Mrs. /Or gender neutral respecive word in korean are gender neutral i.e. 씨 or 님.