Q. Is there a problem with eating honeycomb on Shabbos/ Yom Tov. Is there a difference if I cut a piece and spread the honey using a knife to squeeze the honey out of the comb or if I just cut a small piece and pop the whole thing in my mouth, comb and all.?

A. Shulchan Aruch (O.H. 321:13) rules that when the honeycomb is still attached to the ground, it is forbidden to collect the honey on Shabbat, as it is similar to the prohibited activity of tolesh or detaching, a subcategory of the melacha of kotzer or harvesting.
Mishna Berura, (321: 48, 49) adds that even when the honeycombs are already detached, extracting the honey from them, constitutes also one of the activities Biblically prohibited on Shabbos named “Mefarek,” defined as separating or extracting a natural product from its natural container, peel or shell. (Rabenu Chananel Shabbos 74a, Chaye Adam 14:1). Mefarek is a subcategory of the main melacha of “dosh” or threshing, as in separating the grain from the chaff.
Crushing the honeycomb so that the honey flows out, is included in this prohibition. However, if one crushed the honeycomb thoroughly before Shabbos, one may then use the honey which flows out naturally on Shabbos.
Therefore, one may not use a knife to squeeze the honey out of the honeycomb on Shabbos or Yom Tov. However, one may cut a piece and place it complete in the mouth. Eat the honey and then expel the inedible wax.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a