맙시다 is composed of
말(다) + -(으)ㅂ시다
말다 means "stop doing ..."
Quoted from http://www.livingincmajor.com/my-korean-grammar-usage-note-5-lets
We use -(으)ㅂ시다 to express a suggestion or proposition; to express agreement with or acceptance of another’s suggestion.
01 Let’s…
Verb + (으)ㅂ시다
If the verb stem ends with a vowel (no batchim), -ㅂ시다 is added.
If the verb stem ends with a consonant (with batchim), -읍시다 is added.
가다 (to go) → 갑시다
자다 (to sleep) → 잡시다
마시다 (to drink) → 마십시다
쇼핑하다 (to shop) → 쇼핑합시다
읽다 (to read) → 읽읍시다
먹다 (to eat) → 먹읍시다
02 Irregular Forms
Irregular form ‘ㄷ’
듣다 (to listen) → 들읍시다
걷다 (to walk) → 걸읍시다
묻다 (to ask) → 물읍시다
닫다 (to close) → 닫읍시다
받다 (to receive) → 받읍시다
Irregular form ‘ㄹ’
알다 (to know) → 압시다
살다 (to live) → 삽시다
놀다 (to play) → 놉시다
03 Let’s not…
Verb + 지 맙시다
The negative form is -지 맙시다. It is added directly to the verb stem, regardless of whether the verb stem ends in a vowel or a consonant (with/without batchim).
수영하다 (to swim) → 수영하지 맙시다
듣다 (to listen) → 듣지 맙시다
보다 (to watch) → 보지 맙시다
나가다 (to go out) → 나가지 맙시다
놀다 (to play) → 놀지 맙시다
쓰다 (to write) → 쓰지 맙시다