In the previous mishnah we dealt with two partners in a vineyard, and even so we did not apply 'bereirah'. We were not prepared to establish that what each one ultimately takes for himself is entirely his; rather, each of the partners is required to assume that half of what he holds belonged to his fellow's portion, and we do not say that the portion now in his hands was designated for him from the outset.
Why 'bereirah' applies specifically here:
Unlike the previous mishnah, in the mishnah before us - chapter 6, mishnah 8 - we do apply 'bereirah', and we establish that what each one takes for himself is indeed his. The reason, as the Rav explains, is that in the previous mishnah the division was made after the produce had already been detached and picked, whereas here the division is made while the produce is still attached to the ground, and in such a case we do apply 'bereirah'.
The wording of the mishnah:
"Shenayim shekiblu sadeh be'arisut" - two men who together took a field as sharecroppers, working it on a percentage basis.
"O sheyarshu" - or who inherited a field together.
"O shenishtatfu" - or who became partners in a field.
"Yachol hu lomar" - this refers to a person who is careful about maaser and trustworthy to separate it, while his partner is not careful.
"Tol atah chittim shebimkom peloni va'ani chittim shebimkom peloni" - the partner who does not tithe takes the wheat in one area, and the one who tithes takes the wheat in the other area.
"Atah yayin shebimkom peloni va'ani yayin shebimkom peloni" - and the same with wine: this one takes from one place and that one from another place.
Once the division has been made in this manner, yours is yours and mine is mine, and the one who tithes is not responsible to make sure that maaser was separated from his fellow's portion, since what is in his own hands is his.
The limits of this leniency - dividing two different species:
Even in this case there is a situation in which it is a problem: "Aval lo yomar lo: tol atah chittim va'ani se'orim" - he may not say to his fellow who does not separate maaser that he should take the wheat while he himself takes the barley. Since each of the partners has a share in the wheat and a share in the barley, by taking the wheat for himself he is handing over to his fellow half of the barley that was his and that was coming to him, and he is allowing it to leave his hands without maaser being separated.
And likewise "Tol atah yayin va'ani shemen" - since these are two different species, he had a share in the other species as well, and therefore the responsibility rests upon him to make sure that maaser was separated from what he hands over to his fellow.
In summary: In this mishnah we learned that in dividing a jointly held field - whether through sharecropping, inheritance or partnership - we apply 'bereirah' when the division is made while the produce is still attached to the ground, and therefore each one's portion is considered his from the outset, and the one who tithes bears no responsibility for his fellow's portion. Such a division is valid as long as it is made within the same species (wheat against wheat, wine against wine); but one may not divide one species against another - wheat against barley or wine against oil - since in doing so a person releases from his hands his own share in that species without maaser.