Demai, Mishnah 11. Much like the previous mishnah, which dealt with separating Terumah from produce that is not obligated in Terumah by Torah law on behalf of produce that is obligated, and also the reverse, our mishnah too deals with a similar idea.
The wording of the mishnah and our starting point:
The mishnah opens: "Terumah min hademai al hademai" - what is the ruling of one who separates Terumah from one batch of demai on behalf of another batch of demai, where we are not speaking of one person but of two different amei ha'aretz who are not careful to tithe properly, so that possibly one of them tithed and the other did not.
One point must be established first: when the mishnah here says "Terumah," it means terumas ma'aser, since with demai there is no need to separate Terumah - the amei ha'aretz do separate the Terumah, and only terumas ma'aser still requires separation.
From demai on behalf of demai or on behalf of certain produce:
One who separates terumas ma'aser from demai, which is not obligated in terumas ma'aser by Torah law but only by rabbinic law, and separates it on behalf of certain produce, which is obligated in terumas ma'aser by Torah law since it is Torah level tevel, turns out to be separating Terumah from something that is not obligated in Terumah by Torah law, and making it Terumah for something that requires terumas ma'aser by Torah law. In such a case:
The Terumah he separated does have the status of Terumah, since he declared it to be Terumah.
"Yachzor v'yitrom" - he must separate Terumah again from the certain produce, or from the other batch of demai, since that certain produce, and also the demai on whose behalf the separation was made, is obligated by Torah law, and perhaps ma'aser was never separated from it. Therefore Terumah must be separated a second time from the item on whose behalf the separation was made, even though the first separation retains the status of Terumah.
From obligated produce on behalf of demai:
One who separates from produce that is certainly obligated in terumas ma'aser, and separates it on behalf of demai, which by Torah law is not obligated in terumas ma'aser - the Terumah he designated has the status of Terumah, and it must be given to a kohen. However, the kohen may not eat that terumas ma'aser until he separates terumas ma'aser from it, because it is still obligated by Torah law and is still considered tevel: since he took the terumas ma'aser on behalf of demai, which by Torah law is not obligated in the separation of terumas ma'aser, it turns out that the terumas ma'aser he declared from the certain produce is itself tevel, and terumas ma'aser must be separated from it before the kohen eats it.
A question on the first ruling in the mishnah:
In the first ruling, "Terumah min hademai al hademai," we defined the case as one who takes from demai that is not obligated by Torah law on behalf of other demai that perhaps is obligated by Torah law. But how do we know that it is not the other way around - that the demai from which he takes the Terumah is obligated by Torah law, while the demai on whose behalf he separates is not obligated by Torah law?
The commentators explain that we are not concerned about this possibility, and therefore we rule that the separation counts as Terumah and only the remaining demai requires the separation of Terumah. The reason: regarding demai, most amei ha'aretz do tithe. Accordingly, the assumption is that even though there is a slight concern that this demai is Torah level tevel, on the basic level we assume that by Torah law it is not tevel, and therefore there is no need to separate terumos and ma'asros from it as there is in the reverse case.
In summary: in this mishnah we learned three situations: one who separates from demai on behalf of demai or on behalf of certain produce - his separation is Terumah, but in any event he must separate Terumah again from the item on whose behalf he separated; one who separates from certain produce on behalf of demai - his separation is Terumah that is given to a kohen, but the kohen may not eat it until terumas ma'aser is separated from it; and finally it was explained why we are not concerned about the reverse possibility in the first ruling - because most amei ha'aretz do tithe.