The gemara explains the position of R. Meir who holds that vessels with long handles only require tevila up until the point that the handle serves a function but not beyond that point. The rationale is that since it will be cut off, we view it as if it were already cut off and therefore isn't part of the vessel. The Rosh and Rash in Keilim develop from this mishna an interesting principle. Normally, areas that qualify as beis ha'starim on a person we don't require water to actually touch so long as there is no chatzitza rendering the area fit for water to enter. However, if that were the halacha by keilim as well it wouldn't make sense to simply be tovel the vessel until the point where the handle will be cut, because the point at which it is cut is not fit for bi'as mayim - to touch the water. Clearly, the halacha of beis has'tarim of vessels is that it doesn't even need to be fit for water to touch. However, the Mishna Acrhona (one of the commentaries in taharos) disagrees. He holds that even by keilim there is a requirement that the beis hastarim be ראוי לביאת מים, yet we don't consider the area that would be exposed when it is cut to be a problem because it is the minority of the vessel and people aren't makpid about the handle being there, therefore it isn't a chatzitzah. In truth, Tosafos (d.h. matbil) also considers the handle prior to being cut off to be a problem of chatzitza at the point that it will be cut and therefore makes the case where water can permeate the handle so that it isn't a chatzitzah. See Mayim Rabim pg. 236.