To Mention
To Say, To Eat, To Drink
transitive verb, expression
You've already learned that 口 means "mouth" and here it's followed by the particle に, which pinpoints a location. The verb する means "to do" so you're doing something to your mouth! Logically enough, this expression is used to describe lots of actions that you do with your mouth. It's often used to mean to mention or to say, but with an added descriptive nuance that you've said something accidentally or unexpectedly, maybe something you shouldn't have said! 🙊
It can also mean other things done with the mouth, like to eat and to drink!
くちにする
In this expression, 口 is a standalone vocabulary word, so it uses the same reading that you learned when you learned the vocabulary.
ぜったいにそのなまえを口にしないでね。
Don't ever mention that name, okay?
女王は「好き」と口にした。
The words "I love you" slipped out of the queen's mouth.
王女はおそるおそる玉ねぎを口にした。
The princess ate the onion timidly.