The juice is just contained in the grape (Pesachim 33b)
The gemara on 33b says that according to one opinion the juice inside the grape is separate so when the grape becomes tamei the juice does not automatically become tamei. The gemara though says that if the grape was truma that became tamei we don't allow you to take the juice out of the grape and use it for fear that it may lead "lidei takala" - you may accidentally eat the truma temeia. Therefore the gemara says you need to burn it immediately. The thing that bothered me about this is: How can we burn the entire grape if the juice inside of it is tahor? You're not allowed to burn truma tehora and that's what the juice inside of the grape is!?!
Normally, in Pesachim whenever I've had a question I've just checked the Tzlach and he often asks the question and answers it. So that was the first place I checked but he didn't ask my question this time. He did ask another question though. Rashi in d"h "ksavar mashkin mifkad pakid" explains why the juice doesn't become tamei from the grapes while it's inside. The grape should be a rishon and that should make the juice a sheni. So Rashi says that the reason it doesn't become tamei is because it's not considered food until it actually comes out. The Tzlach asks why is Rashi forced to give this explanation, why couldn't he just simply explain that the juice can't become tamei because the solid in the grape is less than a k'beitza so it can't be metamei the juice? He does not answer the question but leaves it as a "tzaruch iyun."
I was thinking that my question and the Tzlach's could answer the other. The reason you're allowed to burn the liquid inside of the grape is because it's not considered food until it comes out. That's why Rashi wanted to stress that point right at the beginning of the gemara so that you wouldn't be bothered by my question. It's not truma when you're burning it so you're burning the solid of the grape which is truma temeia together with the liquid which isn't truma at all.