Oh no no no, don't do that, please! The sugar in fruit is NOT the same as the white sugar. Fruit is a complex carbohydrate, a GOOD carb. The sugar in fruit is digested much slower than refined sugar, it does not put a burden on your body and cause your body to over use your B-vitamins to digest it (white sugar and other simple carbs do put a burden on your body). Fruits, however, contain everything it needs right in the fruit for your body to digest it properly. Things like white sugar and white flour that's used in so many foods does not contain everything it needs for the body to digest it properly and puts a burden on your body because it has to overwork to digest it. Multi-vitamins are not complete either. You cannot get the same things from a multivitamin that you get from a fruit. Fruit contains something very important, ENZYMES, which MUST be present for any vitamin to work in the body properly or else your body will "borrow" from other sources within your body to complete what's needed for that vitamin to work, which could then lead to deficiencies of other things... For example, citric acid is NOT completely vitamin C, there are other parts of vitamin C that man can not isolate and put into a vitamin. A truly COMPLETE vitamin would only be in the foods that naturally contain them, or the next best thing would be a "whole foods" vitamin (which WOULD be the best kind of vitamin to buy but is usally more expensive). If you completely give up fruit, you are giving up a large part of the "raw part" of your diet. Those enzymes are in raw foods like fruits and vegetables, your body needs them, needs them badly, in order to get rid of acne and stay healthy. And it's not just the vitamins and enzymes that are important, it's also the water and fiber. Many people might disagree with me, but from what I've studied so far I am quite confident that this is very sound advice.... Unless your body has some type of allergic reaction to fruit or a disorder that keeps you from being able to eat it, it would be a horrible thing to give up fruit completely, and I would be willing to bet strongly that your acne would only get worse. Don't give up uncooked vegetables either. You need as much raw food in your diet as you can fit in there (I don't mean to become a vegetarian).
If you had the money, it would be a good idea to buy "whole foods vitamins" instead of a multi-vitamin, and you can also buy enzymes as well. Do some research about this online if you can. But the best thing would be to spend that money on fruits and vegetables and eat them throughout the day as snacks (they certainly won't make you fat). In addition, I know that "hydrogenated" oils are horrible for your body and can certainly lead to acne. If you look at almost any snack food (junk food), you will almost always see it listed as an ingredient, like "hydrogenated soy bean oil" or "partially hydrogenated", not just soybean oil, other hydrogenated oils as well. I would eliminate ALL these as best as you could, or only have them rarely. Of course, there is much more to all this nutrition stuff and how it relates to acne, but some of the the things I've mentioned so far would be the most important.
Again though, many people would disagree with me on some of these things. BUT you have to do the research yourself and test it out and decide for yourself.