Learn Dutch: Het geweld kan mensen doden. - The violence can kill people.

Because the auxiliary verb here is kan (from kunnen). Modal verbs like kunnen, moeten, willen, and mogen always take a bare infinitive without te. The object control rules you are learning only apply to specific verbs like adviseren or dwingen.

Could I use vermoorden instead of doden in this sentence?

It would sound unnatural. Vermoorden specifically means "to murder," which implies conscious, malicious intent by a person. Doden means "to kill" or "to cause death," which is the correct word to use when the subject is an abstract concept or force like het geweld (the violence).

Why does mensen come between the two verbs?

This is the standard "verb brace" word order in Dutch. In a main clause, the conjugated verb (kan) takes the second position, while the infinitive (doden) gets pushed to the very end of the clause. Direct objects like mensen go in the middle.

Abstract nouns often don't need articles. Why use het before geweld here?