The Shulchan Aruch (320) codifies the Torah prohibition of "Sechita," which forbids squeezing grapes and olives on Shabbat. Does this prohibition apply as well to sucking juice from a fruit on Shabbat, or does Halacha distinguish in this regard between squeezing with one's hands and squeezing with one's mouth?
The Hagahot Maimoni (glosses to the Rambam's Mishneh Torah by Rabbi Meir Hakohen, Germany, 13th century), commenting on Hilchot Shabbat (chapter 21), forbids sucking juice on Shabbat, and this is the position as well of the Sefer Yerei'im (Rabbi Eliezer of Metz, France, 1115-1198), in Siman 274. According to this view, it would be forbidden on Shabbat to suck juice from any fruit or other food with absorbed liquid, such as moist meat, sugarcane, and bread that had been dipped in soup. However, the Beit Yosef (commentary to the Tur by Rabbi Yosef Karo, author of the Shulchan Aruch) held (in Siman 320) that sucking the juice from foods does not represent the standard manner of "Sechita," and is thus not included under this prohibition (listen to audio for precise citation).
Rabbi Moshe Halevi, in his work "Menuchat Ahava" (vol. 2, p. 165), cites both views and sides with the lenient position of the Beit Yosef. This is the ruling as well of Chacham Ovadia Yosef, in his work Halichot Olam (vol. 4, p. 106).
Thus, it is permissible on Shabbat to extract liquid with one's mouth from fruits or other foods, such as moist meat, sugarcane, and bread that had been dipped in soup.
