Here is the thing, the body is what does the "detoxifying" not the juice. There is no magic taking place by drinking straight juice. Speaking purely nutritionally, doing a 10 day juice fast is a poor choice for health.
I would hate to see someone watch this movie and think a juice fast is somehow a good idea. It's not. Drinking juice can be a part of a healthy diet but its not the answer by itself.
If you want to get healthy and lose bodyfat there are far more appropriate ways to do it than a juice fast. When exploring this idea you need to understand that if all you consumed is juice at some point you would die of malnutrition, that is fact. You require fat and protein to live. You CAN get that from none meat sources if you choose I'm not here to debate that fact, however unless you know how, you probably won't. This is why many vegans look so sickly, they are malnourished. Not because they are vegan but because they don't know how to get what they need from non-meat sources.
You can live several weeks with no food at all so certainly doing a juice fast for 10 days is likely not going to kill you by any means but it is not the healthiest thing you can do for yourself.