You can cut back or cut down on your coffee - it will mean the same thing and they are both correct.
However, that is not always true.
If I shorten the branches of a bush or a tree, I am cutting them back, not down.
'Cut back' also might imply that you have let something get too far and are reducing it for that reason.
In a movie or story, if the story goes back to an earlier time, we say it cuts back to an earlier scene.
We say someone has been cut down if they have been killed violently by gun or sword.
You hopes can be cut down, but not back.