I believe it's 'grunen' because of strong inflection (there is no definite or indefinite article in the sentence to indicate the gender of Saft like 'der' or 'ein') and since Saft is masculine and accusative, the ending is -en.
Because the 'Orange' in 'Orangensaft' refers to the fruit, not the color. It's a noun and thus become one word, a compound noun, but here 'grünen' is an adjective, so it's two words. If it were juice that happened to have an orange color, I imagine it would be 'orangen Saft'.
For quick reference:
Strong inflections are used when there is no article.
Weak inflections are used when a definite article is used.
Mixed inflections are used when an indefinite article (ein, kein, or any -ein word, including all genitive pronouns acting as possessive adjectives) is used.
If "I have green juice" is correct, then also "I have the green juice"
That is not correct.
The two sentences do not mean the same thing -- "I have the green juice" talks about a specific quantity or kind of green juice that is known to the listener, while "I have green juice" does not.