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.

--I want to reduce the amount of coffee means that you want to not have as much coffee as you normally do on a daily, weekly, monthly, etc., basis. --I want to reduce the amount I intake of coffee means that you want to no put as much coffee as you normally do in your cup, or normally drink ( say in the morning). ->I want to cut back on coffee and I want to cut down on coffee mean the same thing. -> I would say, "I want to cut down on how much coffee I drink." or "I want to cut back on how much coffee I drink".