"Let's not cook animals."
Translation:동물을 요리하지 맙시다.
What is the relationship between 요리하다 and 요리하지? What does 하지 let you do exactly?
I think the -지 ending is a negation. In these sentences it's like a "(let's) not".
That's not quite right. 말다 (conjugated here as 맙시다) is the negation. -지 basically only serves a grammatical function here.