One of thirty-nine Melachot (categories of activity) that are forbidden on Shabbat is "Dash," which means threshing, or extracting kernels of wheat from the chaff. In its broader application, this prohibition forbids extracting any food from the place within which it is embedded ("Mefarek Toleda De’Dash"). This also includes "Sehita," squeezing an object to extract liquids absorbed within it. With regard to grapes and olives, squeezing is forbidden on Shabbat on the level of Torah prohibition. Since olives are grown primarily for their oil and grapes primarily for wine, pressing these fruits for their liquid violates the Torah prohibition of "Dash." And if one violated this prohibition and squeezed a grape or olive, the extracted liquid is forbidden for consumption. When it comes to other fruits, however, extracting juice through squeezing is forbidden on the level of Rabbinic enactment.
The question thus arises as to the permissibility of slicing juicy fruits, such as grapefruits, on Shabbat. When one cuts a grapefruit, it is inevitable that juice will be extracted from the fruit. Moreover, many people enjoy eating grapefruit by digging a spoon into the fruit, which invariably results in the extraction of juice. Is this permissible on Shabbat, or does it violate the Shabbat prohibition of Sehita?
Hacham Ovadia Yosef ruled that one may slice a grapefruit and eat it with a spoon on Shabbat (listen to audio recording for precise citation). Even though this will inevitably extract juice, and is thus a situation of "Pesik Resheh" (an action that inevitably results in a Shabbat prohibition), there is a rule in Halacha allowing a "Pesik Resheh" when it involves a Rabbinic prohibition. As mentioned, extracting juice from fruits other than grapes and olives is forbidden only by force of Rabbinic enactment, and therefore it is permissible to slice fruits even though this will cause juice to be extracted. This applies as well to eating grapefruit with a spoon. As long as one’s intent is to scoop the fruit, and not to extract the juice, he may do so on Shabbat. Of course, it would be forbidden to dig a spoon into a grapefruit with the specific intention of extracting juice. But as long as one’s intent is to remove the fruit from the peel, and not to extract juice, he may eat the grapefruit in this manner on Shabbat.
Rav Yosef Shalom Elyashiv adds another reason to allow eating a grapefruit in this manner on Shabbat. Even when it comes to grapes and olives, Halacha allows squeezing these fruits directly over foods; the prohibition applies only to squeezing them over an empty utensil. Thus, for example, one who prepares food for an infant and wishes to soften it may squeeze some grapes directly onto the food on Shabbat. When one digs a spoon into a grapefruit, the extracted juices remain in the grapefruit, and this is thus a situation of squeezing fruit onto food on Shabbat, which is permissible.
Hacham Ovadia adds that this ruling naturally applies to all fruits; it is permissible to slice any fruit on Shabbat, such as pomegranates and berries. And if some juice from the fruit is left in the plate or bowl in which it was sliced, one may drink that juice, since the fruit was not sliced for the purpose of extracting juice.
Summary: It is permissible to slice fruits, such as grapefruits, on Shabbat even though this will inevitably result in the extraction of some juice. One may also scoop the fruit of a grapefruit with a spoon to eat it, as long as he does not specifically intend to extract juice.