One of the Av Milachos is Tochein, grinding, or making food into very little pieces. The Orchos Shabbos (1:5:9-13) says that mashing something, even if it remains in one clump and not separate pieces, is considered Tochein.He brings from the Rambam that if something, like a potato, became very soft (it must be very soft according to Rav Shlomo Zalman Auerbach) from cooking it is already considered ground and therefore you may mash it. However you must mash it with a fork or spoon and not a special mashing utensil because it would be Uvda D’Chol.
This, he says, only applies to cooked foods but if a banana or avocado become soft without cooking, the issur of grinding still applies. He brings in the footnotes that Rav Moshe Feinstein in the Igros Moshe (4:74) matirs mashing a banana because it remains a single mass and not separate pieces. The Tosefta explicitly says that figs may not be mashed, but Rav Moshe says that his research shows that a fig comes apart while the banana doesn’t.