What happens if a person drinks the juice made from two Devil Fruits? Suppose a person takes two Devil Fruits and extracts the juice from them, and then mixes the juices and then drinks. What will happen?
According to the Devil Fruit wikipedia page:


  Only one bite is needed for the user to gain the power of a Devil Fruit, after which the Devil Fruit becomes a simple, useless, disgusting fruit. Swallowing the fruit whole, as Buggy did, has the same effect,[8] Peeling off the skin and eating it piece by piece, such as Kaku and Kalifa did, also works. After ingesting the fruit, the powers within affect the eater's lineage factor.


So basically the method the fruit is eaten does not matter, whether it be eating it piece by piece, as a whole or as a juice. It is the first bite or sip that is important, because after that the fruit becomes useless. So what this means is that in OP's question the person would basically have eaten two fruits.


  One rumor, as recounted by Jabra, is that Devil Fruits house actual devils that will fight when placed in proximity of one another. The resulting battle would destroy the users' bodies. Nevertheless, Blueno contradicted this claim, stating that Grand Line scientists have noted that the phenomenon of one's body destroying itself only occurs when one consumes two Devil Fruits.[18]


So according to Grand Line scientists, a person that would eat or drink two Devil Fruits would die.