Is it permissible to mash soft foods such as avocado, cooked potatoes or bananas on Shabbat?
One of the thirty-nine "Melachot," or areas of forbidden activity on Shabbat, is "Tohen," grinding. Essentially, grinding means transforming a single object into many objects; when preparing cinnamon, for example, a person takes a cinnamon stick and transforms it into many small particles. As such, this prohibition applies to mashing, as well. When a person mashes a banana, for example, it is only due to the moisture in the banana that it remains a single mass. The act of mashing essentially breaks the banana into many small particles, and these particles are held together by the moisture. Therefore, mashing falls under the category of "Tohen" and is forbidden on Shabbat. (Tosefta Shabbat, Perek 15, Halacha 10.)
However, the Sages permitted mashing soft foods with a fork to prepare them for immediate use. Thus, if one wishes to serve mashed potatoes at his Shabbat meal, he may mash the potatoes immediately prior to the meal to prepare them. Similarly, if one wishes to feed banana to an infant, he may mash the banana just before feeding the infant. One may not, however, mash foods to prepare them for a meal later in the day. This is the ruling of Hacham Ovadia Yosef, in his work Yehave Daat (5:27).
Rabbi Moshe Halevi, in his work Menuhat Ahava, Helek 2, page 278, writes that even when one mashes food for immediate use, he should preferably do so in an unusual manner, such as by using the handle of the fork. Even though one may, strictly speaking, mash foods for immediate use even in standard fashion, it is nevertheless admirable to act stringently in this regard and mash in an unconventional manner, in order to satisfy all opinions.
Summary: Halacha permits mashing soft foods – such as avocado, potatoes and bananas – with a fork on Shabbat for immediate use, but not for use later in the day. When one mashes food for immediate use, some authorities recommend doing so in an unusual manner, such as by using the handle of the fork.