The previous Mishnah listed five categories of people who may not separate Terumah, one of them being the cheresh. The cheresh referred to there is the deaf-mute: someone born deaf, who never heard and therefore never learned to speak. Such a person is considered so lacking in intellectual capacity that he cannot separate Terumah.
The novelty of our Mishnah:
Our Mishnah deals with someone who became deaf rather than being born deaf - a person who is able to speak, because he could hear during the early part of his life. Such a person may separate Terumah, except that ideally he should not do so. The reason is entirely incidental: the obligation to recite a berachah before performing a mitzvah.
The obligation of the berachah and the reason for keeping him away:
Bear in mind that these two matters are independent of one another. Someone who performed any mitzvah - taking the lulav, eating matzah, or any other mitzvah - without a berachah has fully fulfilled the mitzvah on the Torah level; he has simply failed to meet the rabbinic obligation to recite a berachah beforehand. Nevertheless, that rabbinic obligation exists, and a person must fulfill it in the manner the Sages required - and that includes hearing, at the very least, his own berachah. This applies to everyone alike, to the deaf person and to the person who hears perfectly well.
Accordingly, it is not proper to eat an apple and recite the berachah over it while a freight train is passing nearby, or in front of a jet engine, when a person cannot hear his own words. The berachah does not reach his ears, whereas ideally he must hear his own berachah.
From here to the case of the deaf person: he will never be able to hear his own berachos, since he does not hear at all. For this reason the Mishnah says that ideally he should not be the one to separate Terumah, for even though he will say the berachah, he will not hear it, and that is not proper.
It emerges that the law regarding a deaf person who speaks but does not hear divides into two:
Ideally: he should not separate Terumah, because he cannot hear the berachah.
After the fact: if he did separate, his Terumah is valid Terumah, since he is of sound mind and capable of separating.
For wherever the Sages use the term "cheresh" without qualification, as they did in the previous Mishnah, they mean one who neither hears nor speaks - the person born deaf, who therefore never learned to speak, and who is genuinely regarded as lacking intellectual capacity.
A general note on the language of Chazal:
There is a point worth stressing that is very important to know throughout the study of the words of Chazal: when Chazal use sweeping terms such as "always," "forever" and "all," they do not mean it in an absolute, ironclad sense, but rather refer to the overwhelming majority of cases and to the ordinary rule. Therefore it should come as no surprise that there are Mishnayos in which the term "cheresh" is used and the intent is not a deaf-mute but someone who is merely deaf.
The same is true of all rules and principles: wherever Chazal said "always" or "never," there may well be exceptions, and this does not detract from the general formulation - they mean ninety nine percent of cases and the like. So it is in our case as well.
In summary: a deaf person who speaks but does not hear is not like the deaf-mute of the previous Mishnah: he is of sound mind, and therefore if he separated Terumah, his Terumah is valid. Nevertheless, he should not separate Terumah at the outset, and only for an incidental reason - that he cannot hear the berachah he recites, and at the outset one who recites a berachah must hear it. We have also learned a rule in the language of Chazal, that generalizations such as "always" and "all" are stated as the general rule, and therefore the term "cheresh" does not refer in every place specifically to a deaf-mute.