"Let's not leave too much food."
Translation:음식을 너무 많이 남기지 맙시다.
너무 많다 - be too many/be too much
• when placed before a verb, it is used as "adverb" modifying this verb (intensifying its meaning).
Adverb form of 너무 많다 = 너무 많이
너무 많이 남기다 = Leave too much behind
• when placed before a noun, it is used as "adjective" describing this noun.
Adjective form of 너무 많다 = 너무 많은
너무 많은 음식 = excessive/aplenty food
So, your suggestion:
너무 많은 음식을 남기지 맙시다 = Let's not leave behind the excessive (~spare) food
That's not what the example try to convey which is,
음식을 너무 많이 남기지 맙시다 = Let's not leave excessively (too much) food behind.
• -(으)ㅂ시다 - propositive mode. = Let's / Shall we
This pattern is used to make suggestion or an order to a group of at least two speakers in which the speaker is included.
e.g. 점심 식사합시다 - Let's have lunch
• (으)십시오 - Imperative mode, polite but officious style = Do ...
This ,pattern implies an instruction, command or recommendation.
e.g. 거기 서 계시지 마시고 앉으십시오 - Don't stand there, do take a seat.